@string{ACTNUM = "Acta Numerica"} @string{AMC = "Appl. Math. Comput."} @string{ANM = "Appl. Numer. Math."} @string{APMAT = "Appl. Math."} @string{BAMS = "Bull. Amer. Math. Soc."} @string{BIT = "BIT"} @string{BITNM = "BIT Numerical Mathematics"} @string{CANM = "Com. Appl. Num. Meth."} @string{COMPJ = "Comput. J."} @string{CPAM = "Comm. Pure Appl. Math."} @string{CMA = "Computers Math. Applic."} @string{CMMP = "Comput. Math. Math. Phys."} @string{CMAME = "Comput. Methods Appl. Mech. Engrg."} @string{COMP = "Computing"} @string{CPC = "Comput. Phys. Comm."} @string{CRAS = "C.R. Acad. Sci. Paris"} @string{CZMJ = "Czechoslovak Math. J."} @string{DUK = "Duke Math. J."} @string{ETNA = "Electron. Trans. Numer. Anal."} @string{IJHSC = "Intl. J. High Speed Computing"} @string{IJNME = "Internat. J. Numer. Methods Engrg."} @string{IJSA = "Intl. J. Supercomp. Appl."} @string{IMAJ = "IMA J. Appl. Math."} @string{IMAJNA = "IMA J. Numer. Anal."} @string{JACM = "J. ACM"} @string{JCAM = "J. Comput. Appl. Math."} @string{JCP = "J. Comp. Phys."} @string{JIMA = "J. Inst. Maths Applics"} @string{JMAA = "J. Math. Anal. Appl."} @string{JNBS = "J. Res. Natl. Bur. Stand."} @string{JSC = "J. Sci. Comput."} @string{JSM = "J. Sov. Math."} @string{LAA = "Linear Algebra Appl."} @string{MATCOMP = "Math. Comput."} @string{MSB = "Mat. Sb."} @string{NLAA = "Numer. Linear Algebra Appl."} @string{NUMALGO = "Numer. Algorithms"} @string{NUMAT = "Numer. Math."} @string{PJM = "Pacific J. Math."} @string{PAMS = "Proc. Am. Math. Soc."} @string{PARCOMP = "Parallel Comput."} @string{PIEEE = "Proc. IEEE"} @string{PTRSL = "Philos. Trans. R. Soc. Lond."} @string{QAM = "Quart. Appl. Math."} @string{QJMAM = "Quart. J. Mech. Appl. Math."} @string{RMJM = "Rocky Mountain J. Math."} @string{SIAMJ = "J. Soc. Ind. Appl. Math."} @string{SIAP = "SIAM J. Appl. Math."} @string{SIC = "SIAM J. Comput."} @string{SIADM = "SIAM J. Alg. Disc. Meth." } @string{SIMAX = "SIAM J. Matrix Anal. Appl."} @string{SINUM = "SIAM J. Numer. Anal."} @string{SISC = "SIAM J. Sci. Comput."} @string{SISSC = "SIAM J. Sci. Statist. Comput."} @string{SIREV = "SIAM Rev."} @string{TAMS = "Trans. Amer. Math. Soc."} @string{TOMS = "ACM Trans. Math. Soft. (TOMS)"} @string{ZVM = "Zh. Vychisl. Mat. Mat. Fiz."} @article{aa1971, author = "J. O. Aasen", title = "On the reduction of a symmetric matrix to tridiagonal form", journal = BIT, volume = "11", year = "1971", pages = "233-242" } @techreport{ack1994, author = "Y. Achdou and Y. A. Kuznetsov", title = "Algorithms for a non conforming domain decomposition method", institution = "Centre de Mathématiques Appliquées, Ecole Polytechnique", number = "RI 296", year = "1994" } @article{ad1985, author = "L. M. Adams", title = "M-step preconditioned conjugate gradient methods", journal = SISSC, volume = "6", number = "2", year = "1985", pages = "452-463" } @article{adj1986, author = "L. M. Adams and H. F. Jordan", title = "Is {SOR} color blind?", journal = SISSC, volume = "7", number = "2", year = "1986", pages = "490-506" } @article{ado1988, author = "L. M. Adams and E. G. Ong", title = "Additive polynomial preconditioners for parallel computers", journal = PARCOMP, volume = "9", year = "1988", pages = "333-345" } @article{ah1976, author = "G. Advelas and A. Hadjidimos", title = "On improving the convergence rates of extrapolated alternating direction implicit schemes", journal = BIT, volume = "16", year = "1976", pages = "363-373" } @article{ah1981, author = "G. Advelas and A. Hadjidimos", title = "Optimum accelerated overrelaxation method in a special case", journal = MATCOMP, volume = "36", number = "153", year = "1981", pages = "183-187" } @article{ak1988, author = "V. K. Agapov and Y. A. Kuznetsov", title = "On some versions of the domain decomposition method", journal = "Sov. J. Numer. Anal. Math. Modelling", volume = "3", number = "4", year = "1988", pages = "245-265" } @article{abo1988, author = "A. A. Ahac and J. J. Buoni and D. D. Olesky", title = "Stable {LU} factorization of {H}-matrices", journal = LAA, volume = "99", year = "1988", pages = "97-110" } @article{ao1986, author = "A. A. Ahac and D. D. Olesky", title = "A stable method for the {LU} factorization of {M}-matrices", journal = SIADM, volume = "7", number = "3", year = "1986", pages = "368-378" } @article{ala1989, author = "G. Alaghband", title = "Parallel pivoting combined with parallel reduction and fill-in control", journal = PARCOMP, volume = "11", year = "1989", pages = "201-221" } @article{abdp1981, author = "R. E. Alcouffe and A. Brandt and J. E. Dendy and J. W. Painter", title = "The multi-grid method for the diffusion equation with strongly discontinuous coefficients", journal = SISSC, volume = "2", year = "1981", pages = "430-454" } @article{ale1976, author = "G. Alefeld", title = "Zur konvergenz des {P}eaceman-{R}achford verfahrens", journal = NUMAT, volume = "26", year = "1976", pages = "409-419" } @article{alv1976, author = "G. Alefeld and R. S. Varga", title = "Zur konvergenz des symmetrischen relaxationsverfahrens", journal = NUMAT, volume = "25", year = "1976", pages = "291-295" } @article{av1985, author = "G. Alefeld and P. Volkmann", title = "Regular splittings and monotone iteration functions", journal = NUMAT, volume = "46", year = "1985", pages = "213-228" } @article{all1997, author = "F. Alouges and P. Loreaux", title = "Massively parallel preconditioners", journal = NUMALGO, volume = "14", number = "4", year = "1997", pages = "361-375" } @article{als1993, author = "F. L. Alvarado and R. S. Schreiber", title = "Optimal parallel solution of sparse triangular systems", journal = SISC, volume = "14", number = "2", year = "1993", pages = "446-460" } @article{add1996, author = "P. R. Amestoy and T. A. Davis and I. S. Duff", title = "An approximate minimum degree ordering algorithm", journal = SIMAX, volume = "17", number = "4", year = "1996", pages = "886-905" } @phdthesis{am1990, author = "P. R. Amestoy", title = "Factorisation de grandes matrices creuses non symétriques basée sur une méthode multifrontale dans un environnement multiprocesseur", school = "ENSEEIHT", year = "1990", note = "CERFACS Report TH/PA/91/2" } @article{amd1989, author = "P. R. Amestoy and I. S. Duff", title = "Vectorization of a multiprocessor multifrontal code", journal = IJSA, volume = "3", number = "3", year = "1989", pages = "41-59" } @article{abp1993, author = "P. Amodio and L. Brugnano and T. Politi", title = "Parallel factorizations for tridiagonal matrices", journal = SINUM, volume = "30", number = "3", year = "1993", pages = "813-823" } @article{ana1980, author = "I. M. Anand", title = "Numerical stability of nested dissection orderings", journal = MATCOMP, volume = "35", number = "152", year = "1980", pages = "1235-1249" } @techreport{and1988, author = "C. R. Anderson", title = "Manipulating fast solvers, changing their boundary conditions and putting them on multiple processor computers", institution = "Dept. of Mathematics, UCLA", number = "CAM 88-37", year = "1988" } @inproceedings{and1989, author = "C. R. Anderson", title = "Domain decomposition techniques and the solution of {P}oisson's equation in infinite domains", booktitle = "Second International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1989", pages = "129-139" } @techreport{afgr1987, author = "D. V. Anderson and A. R. Fry and R. Gruber and A. Roy", title = "Gigaflop speed algorithm for the direct solution of large block tridiagonal systems in {3D} physics applications", institution = "Lawrence Livermore Nat. Laboratory", number = "UCRL–96034", year = "1987" } @book{abbbd1992, author = "E. Anderson and Z. Bai and C. Bischof and L. S. Blackford and J. Demmel and J. Dongarra and J. {Du Croz} and A. Greenbaum and S. Hammarling and A. McKenney and D. Sorensen", title = "{LAPACK} Users{'} Guide", publisher = "SIAM", edition = "1st", address = "Philadelphia, PA", year = "1992" } @article{ans1989, author = "E. Anderson and Y. Saad", title = "Solving sparse triangular linear systems on parallel computers", journal = IJHSC, volume = "1", number = "1", year = "1989", pages = "73-95" } @techreport{ag1972, author = "R. S. Anderssen and G. H. Golub", title = "Richardson's non-stationary matrix iterative procedure", institution = "Computer Science Dept., Stanford University", number = "STAN-CS-72-304", year = "1972" } @article{anc1994, author = "M. Angelaccio and M. Clajanni", title = "The row/column pivoting strategy on multicomputers", journal = PARCOMP, volume = "20", number = "2", year = "1994", pages = "197–214" } @article{anc1994b, author = "M. Angelaccio and M. Clajanni", title = "Subcube matrix decomposition, a unifying view for {LU} factorization on multicomputers", journal = PARCOMP, volume = "20", number = "2", year = "1994", pages = "257-270" } @article{api1977, author = "C. J. Apelt and L. T. Isaacs", title = "On the estimation of the optimum accelerator for {SOR} applied to finite element methods", journal = CMAME, volume = "12", year = "1977", pages = "383-391" } @inproceedings{ach1983, author = "J. R. Appleyard and I. M. Cheshire", title = "Nested factorisation", booktitle = "SPE 1983 Reservoir Simulation Symposium, San Francisco", note = "paper SPE 12264", year = "1983" } @techreport{acp1981, author = "J. R. Appleyard and I. M. Cheshire and R. K. Pollard", title = "Special techniques for fully implicit simulators", institution = "AERE Harwell", address = "UK", number = "CSS 112", year = "1981" } @article{add1989, author = "M. Arioli and J. W. Demmel and I. S. Duff", title = "Solving sparse linear systems with sparse backward error", journal = SIMAX, volume = "10", number = "2", year = "1989", pages = "165-190" } @article{adnr1992, author = "M. Arioli and I. S. Duff and J. Noailles and D. Ruiz", title = "A block projection method for sparse matrices", journal = SISSC, volume = "13", number = "1", year = "1992", pages = "47-70" } @article{adr1991, author = "M. Arioli and I. S. Duff and D. Ruiz", title = "Stopping criteria for iterative solvers", journal = SIMAX, volume = "13", number = "1", year = "1991", pages = "138-144" } @article{aps1998, author = "M. Arioli and V. Pt{\'a}k and Z. Strako\v{s}", title = "{K}rylov sequences of maximal length and convergence of {GMRES}", journal = BITNM, volume = "38", number = "4", year = "1998", pages = "636-643" } @article{arr1985, author = "M. Arioli and F. Romani", title = "Relations between condition numbers and the convergence of the {J}acobi method for real positive definite matrices", journal = NUMAT, volume = "46", year = "1985", pages = "31-42" } @article{arr1992, author = "M. Arioli and F. Romani", title = "Stability, convergence and conditioning of stationary iterative methods of the form x(i+1)=Px(i)+q for the solution of linear systems", journal = IMAJNA, volume = "12", year = "1992", pages = "21-30" } @article{ar1951, author = "W. E. Arnoldi", title = "The principle of minimized iterations in the solution of the matrix eigenvalue problem", journal = QAM, volume = "9", year = "1951", pages = "17-29" } @phdthesis{ashb1987, author = "S. F. Ashby", title = "Polynomial preconditioning for conjugate gradient methods", school = "Dept. of Computer Science, University of Illinois", year = "1987" } @article{ashb1991, author = "S. F. Ashby", title = "Minimax polynomial preconditioning for {H}ermitian linear systems", journal = SIMAX, volume = "12", number = "4", year = "1991", pages = "766-789" } @inproceedings{abdh1991, author = "S. F. Ashby and P. N. Brown and M. R. Dorr and A. C. Hindmarsh", title = "Preconditioned iterative methods for discretized transport equations", booktitle = "Proc. International Topical Meeting on Advances in Mathematics, Computations, Reactor Physics", publisher = "American Nuclear Society", year = "1991", pages = " " } @techreport{asg1993, author = "S. F. Ashby and M. H. Gutknecht", title = "A matrix analysis of conjugate gradient algorithms", institution = "Lawrence Livermore National Lab.", number = "UCRL-JC-113560", year = "1993" } @techreport{ahms1992, author = "S. F. Ashby and M. J. Holst and T. A. Manteuffel and P. E. Saylor", title = "The role of the inner product in stopping criteria for conjugate gradient iterations", institution = "Lawrence Livermore National Lab.", number = "UCRL-JC-112586", year = "1992" } @article{ahms2001, author = "S. F. Ashby and M. J. Holst and T. A. Manteuffel and P. E. Saylor", title = "The role of the inner product in stopping criteria for conjugate gradient iterations", journal = BITNM, volume = "41", number = "1", year = "2001", pages = "26-52" } @article{amo1991, author = "S. F. Ashby and T. A. Manteuffel and J. S. Otto", title = "A comparison of adaptive {C}hebyshev and least squares polynomial preconditioning for {H}ermitian positive definite linear systems", journal = SISSC, volume = "13", number = "1", year = "1991", pages = "1-29" } @article{ams1989, author = "S. F. Ashby and T. A. Manteuffel and P. E. Saylor", title = "Adaptive polynomial preconditioning for {H}ermitian indefinite linear systems", journal = BIT, volume = "29", year = "1989", pages = "583-609" } @article{ams1990, author = "S. F. Ashby and T. A. Manteuffel and P. E. Saylor", title = "A taxonomy for conjugate gradient methods", journal = SINUM, volume = "27", number = "6", year = "1990", pages = "1542-1568" } @techreport{asc1991, author = "C. C. Ashcraft", title = "A taxonomy of distributed dense {LU} factorization methods", institution = "Boeing Computer Services", number = "ECA–TR–161", year = "1991" } @phdthesis{asc1995, author = "C. C. Ashcraft", title = "A taxonomy of column-based {C}holesky factorizations", school= "Yale University", year = "1995" } @article{asc1995b, author = "C. C. Ashcraft", title = "Compressed graphs and the minimum degree algorithm", journal = SISC, volume = "16", year = "1995", pages = "1404–1411" } @article{asg1989, author = "C. C. Ashcraft and R. G. Grimes", title = "The influence of relaxed supernode partitions on the multifrontal method", journal = TOMS, volume = "15", year = "1989", pages = "291-309" } @article{aglps1987, author = "C. C. Ashcraft and R. G. Grimes and J. G. Lewis and B. W. Peyton and H. D. Simon", title = "Progress in sparse matrix methods for large linear systems on vector supercomputers", journal = IJSA, volume = "1", number = "4", year = "1987", pages = "10-30" } @article{ascg1988, author = "C. C. Ashcraft and R. G. Grimes", title = "On vectorizing incomplete factorization and {SSOR} preconditioners", journal = SISSC, volume = "9", year = "1988", pages = "122-151" } @article{asl1998, author = "C. C. Ashcraft and J. W. H. Liu", title = "Applications of the {Dulmage-Mendelsohn} decomposition and network flow to graph bisection improvement", journal = SIMAX, volume = "19", number = "2", year = "1998", pages = "325-354" } @article{asl1998b, author = "C. C. Ashcraft and J. W. H. Liu", title = "Robust ordering of sparse matrices using multisection", journal = SIMAX, volume = "19", number = "3", year = "1998", pages = "816-832" } @article{ael1990, author = "C. C. Ashcraft and S. C. Eisenstat and J. W. H. Liu", title = "A fan-in algorithm for distributed sparse numerical factorization", journal = SISSC, volume = "11", number = "3", year = "1990", pages = "593-599" } @article{asl1959, author = "E. Asplund", title = "Inverses of matrices \{$a_{ij}$\} which satisfy $a_{ij}=0$ for $j> i+p$", journal = "Math. Scand.", volume = "7", year = "1959", pages = "57-60" } @article{ax1972, author = "O. Axelsson", title = "A generalized {SSOR} method", journal = BIT, volume = "12", year = "1972", pages = "443-467" } @techreport{ax1974, author = "O. Axelsson", title = "On preconditioning and convergence acceleration for sparse matrix problems", institution = "CERN", address = "Geneva, Switzerland", number = "Report 74-10", year = "1974" } @article{ax1976, author = "O. Axelsson", title = "A class of iterative methods for finite element equations", journal = CMAME, volume = "9", year = "1976", pages = "123-137" } @article{ax1979, author = "O. Axelsson", title = "Preconditioning of indefinite problems by regularization", journal = SINUM, volume = "16", number = "1", year = "1979", pages = "58-69" } @article{ax1980, author = "O. Axelsson", title = "Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations", journal = LAA, volume = "29", year = "1980", pages = "1-16" } @article{ax1985, author = "O. Axelsson", title = "A survey of preconditioned iterative methods for linear systems of algebraic equations", journal = BIT, volume = "25", year = "1985", pages = "166-187" } @article{ax1985b, author = "O. Axelsson", title = "Incomplete block matrix factorization preconditioning methods. {T}he ultimate answer?", journal = JCAM, volume = "12", year = "1985", pages = "3-18" } @article{ax1986, author = "O. Axelsson", title = "A general incomplete block matrix factorization method", journal = LAA, volume = "74", year = "1986", pages = "179-190" } @article{ax1987, author = "O. Axelsson", title = "A generalized conjugate gradient, least square method", journal = NUMAT, volume = "51", number = "2", year = "1987", pages = "209-227" } @book{ax1994, author = "O. Axelsson", title = "Iterative Solution Methods", publisher = "Cambridge University Press", year = "1994" } @inproceedings{ax1996, author = "O. Axelsson", title = "Stabilization of algebraic multilevel iteration; additive methods", booktitle = "{AMLI'96: Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications}", editor = "O. Axelsson and B. Polman", publisher = "University of Nijmegen", year = "1996", pages = "49-62." } @book{axb1984, author = "O. Axelsson and V. A. Barker", title = "Finite element solution of boundary value problems", publisher = "Academic Press", year = "1984" } @article{axbi1984, author = "O. Axelsson and S. Brinkkemper and V. P. {Il'in}", title = "On some versions of incomplete block matrix factorization iterative methods", journal = LAA, volume = "58", year = "1984", pages = "3-15" } @article{axe1986, author = "O. Axelsson and V. Eijkhout", title = "A note on the vectorization of scalar recursions", journal = PARCOMP, volume = "3", year = "1986", pages = "73-83" } @inproceedings{axe1987, author = "O. Axelsson and V. Eijkhout", title = "Robust vectorizable preconditioners for three dimensional elliptic difference equations with anisotropy", booktitle = "Algorithms and Applications on Vector and Parallel Computers", editor = "H. J. J. Riele and T. J. Dekker and H. A. van der Vorst", publisher = "Elsevier", year = "1987", pages = "279-306" } @article{axe1991, author = "O. Axelsson and V. Eijkhout", title = "The nested recursive two level factorization method for nine point difference matrices", journal = SISSC, volume = "12", year = "1991", pages = "1373-1400" } @article{axg1977, author = "O. Axelsson and I. Gustafsson", title = "Iterative methods for the solution of the {N}avier equations of elasticity", journal = CMAME, volume = "15", year = "1977", pages = "241-258" } @article{axg1979, author = "O. Axelsson and I. Gustafsson", title = "An iterative solver for a mixed variable variational formulation of the (first) biharmonic problem", journal = CMAME, volume = "20", year = "1979", pages = "9–16" } @article{axg1979b, author = "O. Axelsson and I. Gustafsson", title = "A modified upwind scheme for convective transport equations and the use of a conjugate gradient method for the solution of nonsymmetric systems of equations", journal = JIMA, volume = "23", year = "1979", pages = "321-337" } @article{axg1980, author = "O. Axelsson and I. Gustafsson", title = "On the use of preconditioned conjugate gradient methods for {Red/Black} ordered five point difference schemes", journal = JCP, volume = "35", year = "1980", pages = "284–289" } @article{axl1986, author = "O. Axelsson and G. Lindskog", title = "On the rate of convergence of the preconditioned conjugate gradient method", journal = NUMAT, volume = "48", year = "1986", pages = "499-523" } @article{axl1986b, author = "O. Axelsson and G. Lindskog", title = "On the eigenvalue distribution of a class of preconditioning methods", journal = NUMAT, volume = "48", year = "1986", pages = "479–498" } @article{axl1994, author = "O. Axelsson and H. Lu", title = "A survey of some estimates of eigenvalues and condition numbers for certain preconditioned matrices", journal = JCAM, volume = "80", year = "1994", pages = "241-264" } @article{axm1979, author = "O. Axelsson and N. Munksgaard", title = "A class of preconditioned conjugate gradient methods for the solution of a mixed finite element discretization of the biharmonic operator", journal = IJNME, volume = "14", year = "1979", pages = "1001-1019" } @article{axp1986, author = "O. Axelsson and B. Polman", title = "On approximate factorization methods for block matrices suitable for vector and parallel processors", journal = LAA, volume = "77", year = "1986", pages = "3-26" } @article{axp1988, author = "O. Axelsson and B. Polman", title = "Block preconditioning and domain decomposition methods, {II}", journal = JCAM, volume = "24", year = "1988", pages = "55-72" } @article{axs1978, author = "O. Axelsson and T. Steihaug", title = "Some computational aspects in the numerical solution of parabolic equations", journal = JCAM, volume = "4", number = "2", year = "1978", pages = "129-141" } @article{axv1989, author = "O. Axelsson and P. S. Vassilevski", title = "Algebraic multilevel preconditioning methods, {I}", journal = NUMAT, volume = "56", year = "1989", pages = "157-177" } @article{axv1989b, author = "O. Axelsson and P. S. Vassilevski", title = "A survey of multilevel preconditioned iterative methods", journal = BITNM, volume = "29", number = "4", year = "1989", pages = "769-793" } @article{axv1990, author = "O. Axelsson and P. S. Vassilevski", title = "Algebraic multilevel preconditioning methods, {II}", journal = SINUM, volume = "27", number = "6", year = "1990", pages = "1569-1590" } @article{axv1991, author = "O. Axelsson and P. S. Vassilevski", title = "A black box generalized conjugate gradient solver with inner iterations and variable step preconditioning", journal = SIMAX, volume = "12", year = "1991", pages = "625-644" } @inproceedings{axv1991b, author = "O. Axelsson and P. S. Vassilevski", title = "Algebraic multilevel preconditioning methods {III}", booktitle = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and Y. A. Kuznetsov and G. Meurant and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1991", pages = "163-177" } @article{ay1999b, author = "E. H. Ayachour", title = "Avoiding look-ahead in the {L}anczos method and {P}ad{\'{e}} approximation", journal = APMAT, volume = "26", number = "1", year = "1999", pages = "33-62" } @article{bab1958, author = "O. Babuska", title = "On the {S}chwarz algorithm in the theory of differential equations of mathematical physics", journal = CZMJ, volume = "8", year = "1958", pages = "328-342" } @article{babe1989, author = "O. Babuska and H. C. Elman", title = "Some aspects of parallel implementation of the finite element method on message passing architectures", journal = JCAM, volume = "27", year = "1989", pages = "157-187" } @article{bad1989, author = "L. Badea", title = "A generalization of the {S}chwarz alternating method to an arbitrary number of subdomains", journal = NUMAT, volume = "55", year = "1989", pages = "61-81" } @article{bcgr1998, author = "J. Baglama and D. Calvetti and G. H. Golub and L. Reichel", title = "Adaptively preconditioned {GMRES} algorithms", journal = SISC, volume = "20", number = "1", year = "1998", pages = "243-269" } @article{ba1994, author = "Z. Bai", title = "Error analysis of the {L}anczos algorithm for the nonsymmetric eigenvalue problem", journal = MATCOMP, volume = "62", number = "205", year = "1994", pages = "209-226" } @article{bzz1996, author = "Z. Z. Bai", title = "A class of hybrid algebraic multilevel preconditioning methods", journal = ANM, volume = "19", year = "1996", pages = "389-399" } @article{bag1997, author = "Z. Bai and G. H. Golub", title = "Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices", journal = "Ann. Numer. Math.", volume = "4", year = "1997", pages = "29-38" } @article{bhr1994, author = "Z. Bai and D. Hu and L. Reichel", title = "A {N}ewton basis {GMRES} implementation", journal = IMAJNA, volume = "14", year = "1994", pages = "563-581" } @article{ban1978, author = "A. Banegas", title = "Fast {P}oisson solvers for problems with sparsity", journal = MATCOMP, volume = "32", number = "142", year = "1978", pages = "441-446" } @article{bk1981, author = "R. E. Bank", title = "A comparison of two multi-level iterative methods for nonsymmetric and indefinite elliptic finite element equations", journal = SINUM, volume = "18", year = "1981", pages = "724-743" } @article{bk1996, author = "R. E. Bank", title = "Hierarchical bases and the finite element method", journal = ACTNUM, volume = "5", year = "1996", pages = "1-43" } @article{bkc1993, author = "R. E. Bank and T. F. Chan", title = "An analysis of the composite step biconjugate gradient method", journal = NUMAT, volume = "66", number = "1", year = "1993", pages = "295-319" } @article{bkc1994, author = "R. E. Bank and T. F. Chan", title = "A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems", journal = NUMALGO, volume = "7", number = "1", year = "1994", pages = "1-16" } @article{bdy1988, author = "R. E. Bank and T. F. Dupont and H. Yserentant", title = "The hierarchical basis multigrid method", journal = NUMAT, volume = "52", year = "1988", pages = "427-458" } @article{bks1999, author = "R. E. Bank and R. {Kent Smith}", title = "The incomplete factorization multigraph algorithm", journal = SISC, volume = "20", number = "4", year = "1999", pages = "1349-1364" } @article{bkr1975, author = "R. E. Bank and D. J. Rose", title = "An O($n^2$) method for solving constant coefficient boundary value problems in two dimensions", journal = SINUM, volume = "12", number = "4", year = "1975", pages = "529-540" } @article{bkr1977, author = "R. E. Bank and D. J. Rose", title = "Marching algorithms for elliptic boundary value problems. {I}: the constant coefficient case", journal = SINUM, volume = "14", number = "5", year = "1977", pages = "792-829" } @article{bkr1990, author = "R. E. Bank and D. J. Rose", title = "On the complexity of sparse {G}aussian elimination via bordering", journal = SISSC, volume = "11", number = "1", year = "1990", pages = "145-160" } @article{bks1987, author = "R. E. Bank and R. {Kent Smith}", title = "General sparse elimination requires no permanent integer storage", journal = SISSC, volume = "8", number = "4", year = "1987", pages = "574-584" } @article{bkw1999, author = "R. E. Bank and C. Wagner", title = "Multilevel {ILU} decomposition", journal = NUMAT, volume = "82", number = "4", year = "1999", pages = "543-576" } @inproceedings{bkx1994, author = "R. E. Bank and J. Xu", title = "The hierarchical basis multigrid method and incomplete {LU} decomposition", booktitle = "Proceedings of the Seventh International Conference on Domain Decomposition", editor = "D. E. Keyes and J. Xu", publisher = "American Mathematical Society", year = "1994", pages = "163-173" } @article{bkx1996, author = "R. E. Bank and J. Xu", title = "An algorithm for coarsening unstructured meshes", journal = NUMAT, volume = "73", year = "1996", pages = "1-36" } @article{bad1971, author = "J. Baranger and M. {Duc-Jacquet}", title = "Matrices tridiagonales sym{\'{e}}triques et matrices factorisables", journal = "RIRO", volume = "3", year = "1971", pages = "61-66" } @article{bmr1985, author = "D. Barkai and K. J. M. Moriarty and C. Rebbi", title = "A modified conjugate gradient solver for very large systems", journal = CPC, volume = "36", year = "1985", pages = "1-8" } @article{bar1986, author = "J. L. Barlow", title = "A note on monitoring the stability of triangular decomposition of sparse matrices", journal = SISSC, volume = "7", number = "1", year = "1986", pages = "166-168" } @article{bps1995, author = "S. T. Barnard and A. Pothen and H. Simon", title = "A spectral algorithm for envelope reduction of sparse matrices", journal = NLAA, volume = "2", number = "4", year = "1995", pages = "317-334" } @article{bbder1996, author = "R. Barrett and M. Berry and J. Dongarra and V. Eijkhout and C. Romine", title = "Algorithmic bombardment for the iterative solution of linear systems: a poly-iterative approach", journal = JCAM, volume = "74", number = "1-2", year = "1996", pages = "91-109" } @article{bar1979, author = "W. W. Barrett", title = "A theorem on inverses of tridiagonal matrices", journal = LAA, volume = "27", year = "1979", pages = "211-217" } @article{baf1981, author = "W. W. Barrett and P. J. Feinsilver", title = "Inverses of banded matrices", journal = LAA, volume = "41", year = "1981", pages = "111-130" } @article{baj1984, author = "W. W. Barrett and C. R. Johnson", title = "Determinantal formulae for matrices with sparse inverses", journal = LAA, volume = "56", year = "1984", pages = "73-88" } @article{bjov1987, author = "W. W. Barrett and C. R. Johnson and D. D. Olesky and P. {van den Driessche}", title = "Inherited matrix entries: principal submatrices of the inverse", journal = SIADM, volume = "8", number = "3", year = "1987", pages = "313-322" } @techreport{bm1994, author = "T. Barth and T. A. Manteuffel", title = "Variable metric conjugate gradient methods", institution ="Los Alamos National Lab." , number = "LA-UR-94-1602", year = "1994" } @article{bg1976, author = "V. Barwell and J. A. George", title = "A comparison of algorithms for solving symmetric indefinite systems of linear equations", journal = TOMS, volume = "2", number = "3", year = "1976", pages = "242-251" } @article{bau1963, author = "F. L. Bauer", title = "Optimally scaled matrices", journal = NUMAT, volume = "5", year = "1963", pages = "73-87" } @article{bau1974, author = "F. L. Bauer", title = "Computational graphs and rounding error", journal = SINUM, volume = "11", year = "1974", pages = "87-96" } @article{bea1984, author = "R. Beauwens", title = "Upper eigenvalue bounds for pencils of matrices", journal = LAA, volume = "62", year = "1984", pages = "87-104" } @article{bea1985, author = "R. Beauwens", title = "On {A}xelsson's perturbations", journal = LAA, volume = "68", year = "1985", pages = "221-242" } @article{beb1988, author = "R. Beauwens and M. {Ben Bouzid}", title = "Existence and conditioning properties of sparse approximate block factorizations", journal = SINUM, volume = "25", number = "4", year = "1988", pages = "941-956" } @article{beq1976, author = "R. Beauwens and L. Quenon", title = "Existence criteria for partial matrix factorizations in iterative methods", journal = SINUM, volume = "13", number = "4", year = "1976", pages = "615-643" } @article{bew1989, author = "R. Beauwens and R. Wilmet", title = "Conditioning analysis of positive definite matrices by approximate factorizations", journal = JCAM, volume = "26", number = "3", year = "1989", pages = "257-269" } @article{bgp1988, author = "C. Begue and R. Glowinski and J. Périaux", title = "Détermination d’un opérateur de préconditionnement pour la résolution itérative du problème de {S}tokes dans la formulation d'{H}elmholtz", journal = CRAS, volume = "306", year = "1988", pages = "247–252" } @article{bf1983, author = "A. Behie and P. Forsyth", title = "Comparison of fast iterative methods for symmetric systems", journal = IMAJNA, volume = "3", year = "1983", pages = "41-63" } @book{bel1960, author = "R. Bellman", title = "Introduction to Matrix Analysis", publisher = "Mc Graw-Hill", year = "1960" } @article{ben1965, author = "J. M. Bennett", title = "Triangular factors of modified matrices", journal = NUMAT, volume = "7", year = "1965", pages = "217-221" } @article{bev1972, author = "A. Benson and D. J. Evans", title = "The successive peripheral block overrelaxation method", journal = JIMA, volume = "9", year = "1972", pages = "68-79" } @article{bgo1999, author = "M. Benzi and G. H. Golub", title = "Bounds for the entries of matrix functions with applications to preconditioning", journal = BITNM, volume = "39", number = "3", year = "1999", pages = "417-438" } @article{bt1998, author = "M. Benzi and M. T{\r u}ma", title = "A sparse approximate inverse preconditioner for nonsymmetric linear systems", journal = SISC, volume = "19", number = "3", year = "1998", pages = "968-994" } @article{bt1999, author = "M. Benzi and M. T{\r u}ma", title = "A comparative study of sparse approximate inverse preconditioners", journal = ANM, volume = "30", number = "2-3", year = "1999", pages = "305-340" } @article{bmt1996, author = "M. Benzi and C. D. Meyer and M. T{\r u}ma", title = "A sparse approximate inverse preconditioner for the conjugate gradient method", journal = SISC, volume = "17", number = "5", year = "1996", pages = "1135-1149" } @article{bzvd1999, author = "M. Benzi and D. B. Szyld and A. {Van Duin}", title = "Orderings for incomplete factorization preconditioning of nonsymmetric problems", journal = SISC, volume = "20", number = "5", year = "1999", pages = "1652-1670" } @article{bne1976, author = "A. Berman and M. Neumann", title = "Consistency and splittings", journal = SINUM, volume = "13", number = "6", year = "1976", pages = "877-888" } @book{bp1979, author = "A. Berman and R. J. Plemmons", title = "Nonnegative Matrices in the Mathematical Sciences", publisher = "Academic Press", note = "Reprinted by SIAM", year = "1979" } @article{bsc1990, author = "P. Berman and G. Schnitger", title = "On the performance of the minimum degree ordering for {G}aussian elimination", journal = SIMAX, volume = "11", number = "1", year = "1990", pages = "83-89" } @book{bem1992, author = "C. Bernardi and Y. Maday", title = "Approximations Spectrales de Problèmes aux Limites Elliptiques", publisher = "Springer", year = "1992" } @article{beb1984, author = "P. A. Bernhardt and J. U. Brackbill", title = "Solution of elliptic equations using fast {P}oisson solvers", journal = JCP, volume = "53", year = "1984", pages = "382-394" } @article{bdjs1986, author = "S. Bette and J. C. Diaz and W. R. Jines and T. Steihaug", title = "A block preconditioned conjugate gradient type iterative solver for linear systems in thermal reservoir simulation", journal = JCP, volume = "67", year = "1986", pages = "37-58" } @article{bcr1988, author = "R. Bevilacqua and B. Codenotti and F. Romani", title = "Parallel solution of block tridiagonal linear systems", journal = LAA, volume = "104", year = "1988", pages = "39-57" } @article{bnm1960, author = "W. G. Bickley and J. McNamee", title = "Matrix and other direct methods for the solution of systems of linear difference equations", journal = PTRSL, volume = "252", number = "1005", year = "1960", pages = "69-131" } @article{biv1959, author = "G. Birkhoff and R. S. Varga", title = "Implicit alternating direction methods", journal = TAMS, volume = "92", number = "1", year = "1959", pages = "13-24" } @inproceedings{bvy1962, author = "G. Birkhoff and R. S. Varga and D. M. Young", title = "Alternating direction implicit methods", booktitle = "Advances in Computers", editor = "F. Alt and M. Rubinof", publisher = "Academic Press", year = "1962", pages = "189-273" } @article{bis1990, author = "C. H. Bischof", title = "Incremental condition estimation", journal = SIMAX, volume = "11", number = "2", year = "1990", pages = "312-322" } @article{bj1994, author = "\AA. Bj{\"o}rck", title = "Numerics of {G}ram-{S}chmidt orthogonalization", journal = LAA, volume = "197", year = "1994", pages = "297-316" } @book{bj1996, author = "\AA. Bj{\"o}rck", title = "Numerical Methods for Least squares Problems", publisher = "SIAM", year = "1996" } @article{bjd1983, author = "P. Bj{{\o}}rstad", title = "Fast numerical solution of the biharmonic {D}irichlet problem on rectangles", journal = SINUM, volume = "20", number = "1", year = "1983", pages = "59-71" } @inproceedings{bjs1992, author = "P. Bj{{\o}}rstad and M. Skogen", title = "Domain decomposition algorithms of {S}chwarz type designed for massively parallel computers", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "362-375" } @article{bjw1986, author = "P. Bj{{\o}}rstad and O. B. Widlund", title = "Iterative methods for the solution of elliptic problems on regions partitioned into substructures", journal = SINUM, volume = "23", number = "6", year = "1986", pages = "1097-1120" } @article{bjw1989, author = "P. Bj{{\o}}rstad and O. B. Widlund", title = "To overlap or not to overlap: {A} note on a domain decomposition method for elliptic problems", journal = SISSC, volume = "10", year = "1989", pages = "1053-1061" } @inproceedings{bp1993, author = "J.R. Blair and B. Peyton", title = "An introduction to chordal graphs and clique trees", booktitle = "Graph Theory and Sparse Matrix Computation", editor = "A. George and J. R. Gilbert and J. W.-H. Liu", publisher = "Springer Verlag", year = "1993", pages = "1-29" } @book{bod1959, author = "E. Bodewig", title = "Matrix Calculus", publisher = "North-Holland", edition = "2nd", year = "1959", note = "First edition 1956" } @article{boi1991, author = "R. F. Boisvert", title = "Algorithms for special tridiagonal systems", journal = SISSC, volume = "12", number = "2", year = "1991", pages = "423–442" } @techreport{bbp1978, author = "D. L. Boley and B. L. Buzbee and S. V. parter", title = "On block relaxation techniques", institution = "Mathematics Research Center, University of Wisconsin", number = "MRC TR–1860", year = "1978" } @article{begg1991, author = "D. L. Boley and S. Elhay and G. H. Golub and M. H. Gutknecht", title = "Nonsymmetric {L}anczos and finding orthogonal polynomials associated with indefinite weights", journal = NUMALGO, volume = "1", number = "1", year = "1991", pages = "21-43" } @article{bol1984, author = "J. A. M. Bollen", title = "Numerical stability of descent methods for solving linear equations", journal = NUMAT, volume = "43", year = "1984", pages = "361-377" } @techreport{bh1996, author = "E. G. Boman and B. Hendrickson", title = "A multilevel algorithm for reducing the envelope of sparse matrices", institution = "Computer Science Dept., Stanford University", number = "SCCM-96-14", year = "1996" } @techreport{bm1980, author = "M. Bonnet and G. Meurant", title = "R{\'{e}}solution de syst{\`e}mes d'{\'{e}}quations lin{\'{e}}aires par la m{\'{e}}thode du gradient conjugu{\'{e}} avec pr{\'{e}}conditionnement", institution = "CEA/DAM", number = "N-2159", year = "1980" } @article{bor1989, author = "C. Borgers", title = "The {Neumann-Dirichlet} domain decomposition method with inexact solvers on the subdomains", journal = NUMAT, volume = "55", year = "1989", pages = "123-136" } @article{bor1990, author = "C. Borgers", title = "Domain imbedding methods for the {S}tokes equation", journal = NUMAT, volume = "57", year = "1990", pages = "435-451" } @article{bow1990, author = "C. Borgers and O. B. Widlund", title = "On finite element domain imbedding methods", journal = SINUM, volume = "27", year = "1990", pages = "963-978" } @article{bov1981, author = "E. F. Bota and A. E. Veldman", title = "On local relaxation methods and their application to convection-diffusion equations", journal = JCP, volume = "48", year = "1981", pages = "127-149" } @article{bot1975, author = "Z. Bothe", title = "Bounds for rounding errors in the {G}aussian elimination for band systems", journal = JIMA, volume = "16", year = "1975", pages = "133-142" } @article{btw1993, author = "E. F. F. Botta and F. W. Wubs", title = "The convergence behaviour of iterative methods on severely stretched grids", journal = IJNME, volume = "36", year = "1993", pages = "3333-3350" } @article{bbs1973, author = "A. Bracha-Barak and P. E. Saylor", title = "A symmetric factorization procedure for the solution of elliptic boundary value problems", journal = SINUM, volume = "10", number = "1", year = "1973", pages = "190-206" } @article{brs1981, author = "D. Braess", title = "The contraction number of a multigrid method for solving the {P}oisson equation", journal = NUMAT, volume = "37", year = "1981", pages = "387-404" } @article{brs1995, author = "D. Braess", title = "Towards algebraic multigrid for elliptic problems of second order", journal = "Computing", volume = "55", year = "1995", pages = "379-393" } @book{bmb1993, author = "J. H. Bramble", title = "Multigrid Methods", publisher = "Longman Scientific \& Technical", address = "Essex, UK", note = "Pitman Research Notes in Mathematical Sciences Vol. 294", year = "1993" } @article{beps1988, author = "J. H. Bramble and R. E. Ewing and J. E. Pasciak and A. H. Schatz", title = "A preconditioning technique for the efficient solution of problems with local grid refinement", journal = CMAME, volume = "67", year = "1988", pages = "149-159" } @techreport{brp1984, author = "J. H. Bramble and J. E. Pasciak", title = "Preconditioned iterative methods for nonselfadjoint or indefinite elliptic boundary value problems", institution = "Dept. of Computer Science, Yale University", number = "YALEU/DCS/RR 309", year = "1984" } @article{brp1992, author = "J. H. Bramble and J. E. Pasciak", title = "The analysis of smoothers for multigrid algorithms", journal = MATCOMP, volume = "58", year = "1992", pages = "467-488" } @article{bpst1989, author = "J. H. Bramble and J. E. Pasciak and P. M. Sammon and V. Thomée", title = "Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data", journal = MATCOMP, volume = "52", number = "186", year = "1989", pages = "339-367" } @article{bps1986, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", title = "An iterative method for elliptic problems on regions partitioned into substructures", journal = MATCOMP, volume = "46", number = "174", year = "1986", pages = "361-369" } @article{bps1986b, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", title = "The construction of preconditioners for elliptic problems by substructuring {I}", journal = MATCOMP, volume = "47", number = "175", year = "1986", pages = "103-134" } @article{bps1987, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", title = "The construction of preconditioners for elliptic problems by substructuring {II}", journal = MATCOMP, volume = "49", number = "179", year = "1987", pages = "1-16" } @article{bps1988, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", title = "The construction of preconditioners for elliptic problems by substructuring {III}", journal = MATCOMP, volume = "51", number = "184", year = "1988", pages = "415-430" } @article{bps1989, author = "J. H. Bramble and J. E. Pasciak and A. H. Schatz", title = "The construction of preconditioners for elliptic problems by substructuring {IV}", journal = MATCOMP, volume = "53", number = "187", year = "1989", pages = "1-24" } @article{bpw1991b, author = "J. H. Bramble and J. E. Pasciak and J. P. Wang and J. Xu", title = "Convergence estimates for product iterative methods with applications to domain decomposition", journal = MATCOMP, volume = "57", number = "195", year = "1991", pages = "1-21" } @article{bpw1991, author = "J. H. Bramble and J. E. Pasciak and J. P. Wang and J. Xu", title = "Convergence estimates for multigrid algorithms without regularity assumptions", journal = MATCOMP, volume = "57", number = "195", year = "1991", pages = "23-45" } @article{bpx1988, author = "J. H. Bramble and J. E. Pasciak and J. Xu", title = "The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems", journal = MATCOMP, volume = "51", year = "1988", pages = "389-414" } @article{bpx1990, author = "J. H. Bramble and J. E. Pasciak and J. Xu", title = "Parallel multilevel preconditioners", journal = MATCOMP, volume = "55", number = "191", year = "1990", pages = "1-22" } @article{bpx1991, author = "J. H. Bramble and J. E. Pasciak and J. Xu", title = "The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms", journal = MATCOMP, volume = "56", year = "1991", pages = "1-34" } @article{bra1992, author = "C. W. Brand", title = "An incomplete factorization preconditioning using repeated {R}ed/{B}lack ordering", journal = NUMAT, volume = "61", year = "1992", pages = "433-454" } @inproceedings{bra1973, author = "A. Brandt", title = "Multi{-}level adaptive technique ({MLAT}) for fast numerical solution to boundary value problems", booktitle = "Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics", editor = "H. Cabannes and R. Temam", note = "Lecture Notes in Physics 18", publisher = "Springer", year = "1973", pages = "82-89" } @article{bra1977, author = "A. Brandt", title = "Multi{-}level adaptive solutions to boundary{-}value problems", journal = MATCOMP, volume = "31", year = "1977", pages = "333-390" } @inproceedings{bra1982, author = "A. Brandt", title = "Guide to multigrid development", booktitle = "Multigrid Methods, Proceedings of the Koln-Porz Conference", editor = "W. Hackbusch and U. Trottenberg", note = "Lecture Notes in Mathematics 960", publisher = "Springer", year = "1982", pages = "220-312" } @article{bra1986, author = "A. Brandt", title = "Algebraic multigrid theory: {T}he symmetric case", journal = AMC, volume = "19", year = "1986", pages = "23-56" } @article{bra1994, author = "A. Brandt", title = "Rigorous quantitative analysis of multigrid, {I}: {C}onstant coefficients two{-}level cycle with {$L_2$}-norm", journal = SINUM, volume = "31", year = "1994", pages = "1695-1730" } @inproceedings{brd1994, author = "A. Brandt and B. Diskin", title = "Multigrid solvers on decomposed domains", booktitle = "Sixth International Conference on Domain Decomposition", editor = "A. Quaterroni and J. Périaux and Y. A. Kuznetsov and O. B. Widlund", publisher = "American Mathematical Society", year = "1994", pages = "135-155" } @article{bgw1970, author = "R. K. Brayton and F. G. Gustavson and R. A. Willoughby", title = "Some results on sparse matrices", journal = MATCOMP, volume = "24", number = "115", year = "1970", pages = "937-954" } @article{brn1996, author = "S. C. Brenner", title = "Preconditioning complicated finite elements by simple finite elements", journal = SISC, volume = "17", year = "1996", pages = "1269-1274" } @inproceedings{br1991, author = "C. Brezinski", title = "Biorthogonality and conjugate gradient-type algorithms", booktitle = "Contributions in Numerical Mathematics", editor = "R. P. Agarwal", publisher = " World Scientific", year = "1991", pages = "55-70" } @techreport{br1995, author = "C. Brezinski", title = "Hybrid procedures and semi-iterative methods for linear systems", institution = "Université de Lille", number = "?", year = "1995" } @incollection{br1998, author = "C. Brezinski", title = "Hybrid methods for solving systems of equations", booktitle = "NATO ASI Series C Mathematical and Physical Sciences - Advanced Study Institute", publisher = "NATO", volume = "508", year = "1998", pages = "271-290" } @article{brz1994b, author = "C. Brezinski and M. Redivo-Zaglia", title = "Treatment of near-breakdown in the {CGS} algorithm", journal = NUMALGO, volume = "7", year = "1994", pages = "33-73" } @article{brz1994a, author = "C. Brezinski and M. Redivo-Zaglia", title = "Hybrid procedures for solving linear systems", journal = NUMAT, volume = "67", year = "1994", pages = "1-19" } @article{bs1991, author = "C. Brezinski and H. Sadok", title = "Avoiding breakdown in the {CGS} algorithm", journal = NUMALGO, volume = "1", year = "1991", pages = "199-206" } @article{bs1993, author = "C. Brezinski and H. Sadok", title = "Lanczos-type algorithms for solving systems of linear equations", journal = ANM, volume = "11", year = "1993", pages = "443-473" } @article{brz1995, author = "C. Brezinski and M. Redivo-Zaglia", title = "Look-ahead in {BiCGstab} and other methods for linear systems", journal = BIT, volume = "35", year = "1995", pages = "169-201" } @article{brs1991, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "Avoiding breakdown and near-breakdown in {L}anczos type algorithms", journal = NUMALGO, volume = "1", year = "1991", pages = "261-284" } @article{brs1991b, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "Addendum to ``{A}voiding breakdown and near-breakdown in {L}anczos type algorithms'' ", journal = NUMALGO, volume = "2", year = "1992", pages = "133-136" } @article{brs1992, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "A breakdown-free {L}anczos type algorithm for solving linear systems", journal = NUMAT, volume = "63", year = "1992", pages = "29-38" } @article{brs1997, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "Breakdowns in the implementation of the {L}anczos method for solving linear systems", journal = CMA, volume = "33", number = "1", year = "1997", pages = "31-44" } @article{brs1999, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "New look-ahead {L}anczos-type algorithms for linear systems", journal = NUMAT, volume = "83", number = "1", year = "1999", pages = "53-85" } @book{brg1987, author = "W. L. Briggs", title = "A Multigrid Tutorial", year = "1987", publisher = "SIAM" } @article{brh1990, author = "W. L. Briggs and V. E. Henson", title = "{FFT} as a multigrid algorithm", journal = SIREV, volume = "32", year = "1990", pages = "252-261" } @article{brh1993, author = "W. L. Briggs and V. E. Henson", title = "Wavelets and multigrid", journal = SISC, volume = "14", year = "1993", pages = "506–510" } @phdthesis{brk1984, author = "S. Brinkkemper", title = "Two classes of preconditioning matrices", school = "Dept. of Informatics, Catholic University of Nijmegen", year = "1984" } @techreport{brk1985, author = "S. Brinkkemper", title = "A class of incomplete block factorization methods", institution = "Catholic University of Nijmegen", number = "71", year = "1985" } @article{bgp1987, author = "M. O. Bristeau and R. Glowinski and J. Périaux", title = "Numerical methods for the {Navier-Stokes} equations", journal = "Computer Physics Reports", volume = "6", year = "1987", pages = "73-187" } @article{brow1991, author = "P. N. Brown", title = "A theoretical comparison of the {A}rnoldi and {GMRES} algorithms", journal = SISSC, volume = "12", number = "1", year = "1991", pages = "58-78" } @article{bry1973, author = "C. G. Broyden", title = "Some condition number bounds for the {G}aussian elimination process", journal = JIMA, volume = "12", year = "1973", pages = "273-286" } @article{btw1990, author = "A. M. Bruaset and A. Tveito and R. Winther", title = "On the stability of relaxed incomplete {LU} factorizations", journal = MATCOMP, volume = "54", number = "190", year = "1990", pages = "701-719" } @book{brt1995, author = "A. M. Bruaset", title = "A Survey of Preconditioned Iterative Methods", note = "Vol. 328", publisher = "CRC Press", year = "1995" } @article{brm1990, author = "L. Brugnano and M. Marrone", title = "Vectorization of some block preconditioned conjugate gradient methods", journal = PARCOMP, volume = "14", year = "1990", pages = "191-198" } @article{brs1989, author = "G. Brussino and V. Sonnad", title = "A comparison of direct and preconditioned iterative techniques for sparse unsymmetric systems of linear equations", journal = IJNME, volume = "28", year = "1989", pages = "801-815" } @article{bue1973, author = "B. Bukhberger and G. A. {Emel'Yanenko}", title = "Methods of inverting tridiagonal matrices", journal = CMMP, volume = "13", year = "1973", pages = "10–20" } @article{bul1960, author = "N. I. Buleev", title = "A numerical method for the solution of two-dimensional and three-dimensional equations of diffusion", journal = MSB, volume = "51", year = "1960", note = "(in Russian)", pages = "227-238" } @article{bu1971, author = "J. R. Bunch", title = "Analysis of the diagonal pivoting method", journal = SINUM, volume = "8", number = "4", year = "1971", pages = "656-680" } @inproceedings{bu1973, author = "J. R. Bunch", title = "Complexity of sparse elimination", booktitle ="Complexity of Sequential and Parallel Numerical Algorithms" , editor = "J. F. Traub", publisher = "Academic Press", year = "1973", pages = "197-220" } @article{bu1974, author = "J. R. Bunch", title = "Partial pivoting strategies for symmetric matrices", journal = SINUM, volume = "11", number = "3", year = "1974", pages = "521-528" } @article{bu1974b, author = "J. R. Bunch", title = "Analysis of sparse elimination", journal = SINUM, volume = "11", number = "5", year = "1974", pages = "847-873" } @article{bu1987, author = "J. R. Bunch", title = "The weak and strong stability of algorithms in numerical linear algebra", journal = LAA, volume = "88", year = "1987", pages = "49-66" } @article{bdv1989, author = "J. R. Bunch and J. W. Demmel and C. F. {Van Loan}", title = "The strong stability of algorithms for solving symmetric linear systems", journal = SIMAX, volume = "10", number = "4", year = "1989", pages = "494-499" } @article{buh1974, author = "J. R. Bunch and J. E. Hopcroft", title = "Triangular factorization and inversion by fast matrix multiplication", journal = MATCOMP, volume = "28", number = "125", year = "1974", pages = "231-236" } @article{bka1977, author = "J. R. Bunch and L. Kaufman", title = "Some stable methods for calculating inertia and solving symmetric linear systems", journal = MATCOMP, volume = "31", number = "137", year = "1977", pages = "63-179" } @article{bup1971, author = "J. R. Bunch and B. N. Parlett", title = "Direct methods for solving symmetric indefinite systems of linear equations", journal = SINUM, volume = "8", number = "4", year = "1971", pages = "639-655" } @book{bur1976, author = "J. R. Bunch and D. J. Rose", title = "Sparse Matrix Computations", publisher = "Academic Press", year = "1976" } @techreport{bun1969, author = "O. Buneman", title = "A compact non-iterative {P}oisson solver", institution = "Stanford University Institute for Plasma Research, Stanford University", number = "294", year = "1969" } @article{buo1990, author = "J. J. Buoni", title = "A stable method for the incomplete factorization of {H}-matrices", journal = LAA, volume = "129", year = "1990", pages = "143-154" } @incollection{buv1979, author = "J. J. Buoni and R. S. Varga", title = "A theorem of {Stein-Rosenberg} type", booktitle = "Computer Methods for Partial Differential Equations {III}", publisher = "IMACS", year = "1979", pages = "11-12" } @article{bul1986, author = "I. W. Burgess and P. K. F. Lai", title = "A new node renumbering algorithm for bandwidth reduction", journal = IJNME, volume = "23", year = "1986", pages = "1693-1704" } @article{bepw1998, author = "K. Burrage and J. Erhel and B. Pohl and A. Williams", title = "A deflation technique for linear systems of equations", journal = SISC, volume = "19", number = "4", year = "1998", pages = "1245-1260" } @article{buz1973, author = "B. L. Buzbee", title = "A fast {P}oisson solver amenable to parallel computation", journal = "IEEE Trans. on Comp.", volume = "22", number = "8", year = "1973", pages = "793-796" } @article{bud1974, author = "B. L. Buzbee", title = "The direct solution of the biharmonic equation on rectangular regions and the {P}oisson equation on irregular regions", journal = SINUM, volume = "11", number = "4", year = "1974", pages = "753–763" } @article{bgn1970, author = "B. L. Buzbee and G. H. Golub and C. W. Nielson", title = "On direct methods for solving {Poisson}'s equations", journal = SINUM, volume = "7", number = "4", year = "1970", pages = "627-656" } @article{bdgg1971, author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H. Golub", title = "The direct solution of the discrete {Poisson} equation on irregular regions", journal = SINUM, volume = "8", number = "4", year = "1971", pages = "722-736" } @inproceedings{cgk1992, author = "X.-C. Cai and W. D. Gropp and D. E. Keyes", title = "A comparison of some domain decomposition algorithms for nonsymmetric elliptic problems", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "224–234" } @article{cw1992, author = "X.-C. Cai and O. B. Widlund", title = "Domain decomposition algorithms for indefinite elliptic problems", journal = SISSC, volume = "13", number = "1", year = "1992", pages = "243-258" } @article{cx1992, author = "X.-C. Cai and J. Xu", title = " A preconditioned {GMRES} method for nonsymmetric or indefinite problems", journal = MATCOMP, volume = "59", year = "1992", pages = "311-319" } @article{clmm1994, author = "Z. Cai and R. D. Lazarov and T. A. Manteuffel and S. F. McCormick", title = "First order system least squares for second-order partial differential equations: {Part I}", journal = SINUM, volume = "31", year = "1994", pages = "1785-1802" } @article{cm1989, author = "Z. Cai and S. F. McCormick", title = "Computational complexity of the {S}chwarz alternating procedure", journal = IJHSC, volume = "1", year = "1989", pages = "1-28" } @article{cgr1994, author = "D. Calvetti and G. H. Golub and L. Reichel", title = "An adaptive {C}hebyshev iterative method for nonsymmetric linear systems based on modified moments", journal = NUMAT, volume = "67", number = "11", year = "1994", pages = "21-40" } @article{crs1994, author = "D. Calvetti and L. Reichel and D. C. Sorensen", title = "An implicitly restarted {L}anczos method for large symmetric eigenvalue problems", journal = ETNA, volume = "2", year = "1994", pages = "1-21" } @article{ch1966, author = "P. Camion and A. J. Hoffman", title = "On the nonsingularity of complex matrices", journal = PJM, volume = "17", number = "2", year = "1966", pages = "211-214" } @article{cikm1996, author = "S. L. Campbell and I. C. F. Ipsen and C. T. Kelley and C. D. Meyer", title = "{GMRES} and the minimal polynomial", journal = BITNM, volume = "36", number = "4", year = "1996", pages = "664-675" } @techreport{cad1995, author = "Y. E. Campbell and T. A. Davis", title = "Incomplete {LU} factorization: a mutifrontal approach", institution = "Computer Science Dept., University of Florida", number = "TR-95-024", year = "1995" } @article{cfu1988, author = "C. Canuto and D. Funaro", title = "The {S}chwarz algorithm for spectral methods", journal = SINUM, volume = "25", number = "1", year = "1988", pages = "24-40" } @techreport{cgt1996, author = "F. Cao and J. R. Gilbert and S.-H. Teng", title = "Partitioning meshes with lines and planes", institution = "Xerox Parc, Palo Alto", number = "CSL-96-01", year = "1996" } @article{cg1992, author = "C. Carlenzoli and P. Gervasio", title = "Effective numerical algorithms for the solution of algebraic systems arising in spectral methods", journal = ANM, volume = "10", number = "2", year = "1992", pages = "87-113" } @article{crrs1989, author = "P. Carnevali and G. Radicati and Y. Robert and P. Sguazzero", title = "Efficient {F}ortran implementation of the {G}aussian elimination and {H}ouseholder reduction algorithms on the {IBM} 3090 vector multiprocessor", journal = "ESAIM: Mathematical Modelling and Numerical Analysis", volume = "23", number = "1", year = "1989", pages = "63-86" } @article{crr1991, author = "R. Carter", title = "{Y-MP} floating point and {C}holesky factorization", journal = IJHSC, volume = "3", number = "3", year = "1991", pages = "215-222" } @phdthesis{cah1997, author = "L. M. Carvalho", title = "Preconditioned {S}chur complement methods in distributed memory environments", school = "INPT Toulouse", year = "1997", note = "CERFACS report TH/PA/97/41" } @techreport{cc1995, author = "F. Chaitin-Chatelin", title = "Le calcul qualitatif. {C}omment donner un sens à des résultats faux ?", institution = "CERFACS", number = "TR/PA/95/10", year = "1995" } @book{ccf1996, author = "F. Chaitin-Chatelin and V. Frayss{\'{e}}", title = "Lectures on Finite Precision Computations", publisher = "SIAM", year = "1996" } @article{ch1984, author = "T. F. Chan", title = "On the existence and computation of {LU} factorizations with small pivots", journal = MATCOMP, volume = "42", number = "168", year = "1984", pages = "535-547" } @article{ch1987, author = "T. F. Chan", title = "Analysis of preconditioners for domain decomposition", journal = SINUM, volume = "24", number = "2", year = "1987", pages = "382-390" } @inproceedings{ch1989, author = "T. F. Chan", title = "Domain decomposition algorithms and computational fluid dynamics", booktitle = "Parallel Computing: Issues in Applied Research and Development", editor = "J. J. Dongarra and I. S. Duff and P. Gaffney and S. McKee", publisher = "Ellis Horwood", year = "1989", pages = "65-82" } @article{cha1991, author = "T. F. Chan", title = "Fourier analysis of relaxed incomplete factorization preconditioners", journal = SISSC, volume ="12", year = "1991", pages = "668-680" } @article{ce1989, author = "T. F. Chan and H. Elman", title = "Fourier analysis of iterative methods for elliptic problems", journal = SIREV, volume = "31", number = "1", year = "1989", pages = "20-49" } @article{cf1988, author = "T. F. Chan and D. E. Foulser", title = "Effectively well conditioned linear systems", journal = SISSC, volume = "9", year = "1988", pages = "963-969" } @article{cgsst1994, author = "T. F. Chan and E. Gallopoulos and V. Simoncini and T. Szeto and C. H. Tong", title = "A quasi-minimal residual variant of the {Bi-CGStab} algorithm for nonsymmetric systems", journal = SISC, volume = "15", number = "2", year = "1994", pages = "338-347" } @techreport{cgt1995, author = "T. F. Chan and J. R. Gilbert and S.-H. Teng", title = "Geometric spectral partitioning", institution = "Xerox Parc, Palo Alto", number = "?", year = "1995" } @book{cgpw1988, author = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund Eds.", title = "Second International Symposium on Domain Decomposition Methods for Partial Differential Equations", publisher = "SIAM", year = "1989" } @book{cgpw1990, author = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund Eds.", title = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", publisher = "SIAM", year = "1990" } @techreport{cgo1988, author = "T. F. Chan and D. Goovaerts", title = "{Schwarz=Schur}: overlapping versus non overlapping domain decomposition", institution = "Dept.of Mathematics, UCLA", number = "CAM 88-21", year = "1988" } @article{cgo1990, author = "T. F. Chan and D. Goovaerts", title = "A note on the efficiency of domain decomposed incomplete factorizations", journal = SISSC, volume = "11", number = "4", year = "1990", pages = "794-803" } @article{cgo1990b, author = "T. F. Chan and D. Goovaerts", title = "On the relationship between overlapping and nonoverlapping domain decomposition methods", journal = SIMAX, volume = "13", year = "1990", pages = "663-670" } @techreport{cho1990, author = "T. F. Chan and T. Y. Hou", title = "Domain decomposition interface preconditioners for general second order elliptic problems", institution = "Dept. of Mathematics, UCLA", number = "CAM 88-16", year = "1990" } @article{chl1991, author = "T. F. Chan and T. Y. Hou and P. L. Lions", title = "Geometry related convergence results for domain decomposition algorithms", journal = SINUM, volume = "28", number = "2", year = "1991", pages = "378–391" } @inproceedings{chk1990, author = "T. F. Chan and D. E. Keyes", title = "Interface preconditionings for domain decomposed convection-diffusion operators", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1990", pages = "245-262" } @article{ckt1989, author = "T. F. Chan and C. C. J. Kuo and C. Tong", title = "Parallel elliptic preconditioners: {F}ourier analysis and performance on the {C}onnection {M}achine", journal = CPC, volume = "53", year = "1989", pages = "237–252" } @article{ckt1990, author = "T. F. Chan and C. C. J. Kuo and C. Tong", title = "Multilevel filtering preconditioners", journal = SIMAX, volume = "11", number = "3", year = "1990", pages = "403-429" } @inproceedings{cma1991, author = "T. F. Chan and T. Mathew", title = "An application of the probing technique to the vertex space method in domain decomposition", booktitle = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and Y. A. Kuznetsov and G. Meurant and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1991", pages = "101-111" } @article{cma1992, author = "T. F. Chan and T. Mathew", title = "The interface probing in domain decomposition", journal = SIMAX, volume = "13", year = "1992", pages = "212-238" } @article{cma1992c, author = "T. F. Chan and T. Mathew", title = "Domain decomposition algorithms", journal = ACTNUM, volume = "3", year = "1992", pages = "61-143" } @inproceedings{cma1992b, author = "T. F. Chan and T. Mathew", title = "Fourier and probe variants of the vertex space domain decomposition algorithm", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "236-249" } @techreport{cm1990, author = "T. F. Chan and G. Meurant", title = "Fourier analysis of block preconditioners", institution = "University of California, Los Angeles", number = "CAM 90-04", year = "1990" } @techreport{cre1985, author = "T. F. Chan and D. C. Resasco", title = "A survey of preconditioners for domain decomposition", institution = "Dept. of Computer Science, Yale University", number = "YALEU/DCS/RR-414", year = "1985" } @article{cre1986, author = "T. F. Chan and D. C. Resasco", title = "Generalized deflated block elimination", journal = SINUM, volume = "23", number = "5", year = "1986", pages = "913-924" } @inproceedings{cre1987, author = "T. F. Chan and D. C. Resasco", title = "Analysis of domain decomposition preconditioners on irregular regions", booktitle = "Proceedings of the Sixth IMACS Int'l Symp. on Computer Methods for Partial Differential Equations", editor = "R. Vichnevetsky and R. Stepleman", publisher = "IMACS", year = "1987", pages = "317-322" } @article{cre1987b, author = "T. F. Chan and D. C. Resasco", title = "A domain-decomposed fast {P}oisson solver on a rectangle", journal = SISSC, volume = "8", number = "1", year = "1987", pages = "s14-s26", note = "Errata, SISSC, 8(3), p.~457" } @inproceedings{cre1988, author = "T. F. Chan and D. C. Resasco", title = "A framework for the analysis and construction of domain decomposition preconditioners", booktitle = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and G. H. Golub and G. Meurant and J. Périaux", publisher = "SIAM", year = "1988", pages = "217-230" } @inproceedings{csm1994, author = "T. F. Chan and B. F. Smith", title = "Domain decomposition and multigrid algorithms for elliptic problems on unstructured meshes", booktitle = "Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition", editor = "D. E. Keyes and J. Xu", publisher = "American Mathematical Society", year = "1994", pages = "175-189." } @techreport{ctu1989, author = "T. F. Chan and R. S. Tuminaro", title = "Analysis of a parallel multigrid algorithm", institution = "University of California, Los Angeles", number = "CAM 89-29", year = "1989" } @techreport{cvdv1994, author = "T. F. Chan and H. A. {van der Vorst}", title = "Approximate and incomplete factorizations", institution = "Dept. of Mathematics, University of Utrecht", number = "871", year = "1994" } @article{chv1995, author = "T. F. Chan and P. S. Vassilevski", title = "A framework for block {ILU} factorizations using block-size reduction", journal = MATCOMP, volume = "64", number = "209", year = "1995", pages = "129-156" } @article{cw1997, author = "T. F. Chan and W. L. Wan", title = "Analysis of projection methods for solving linear systems with multiple right-hand sides", journal = SISC, volume = "18", number = "6", year = "1997", pages = "1698-1721" } @article{cwy1997, author = "T. F. Chan and Q. Ye", title = "A mixed product {K}rylov subspace method for solving nonsymmetric linear systems", journal = "Asian J. Math.", volume = "1", number = "3", year = "1997", pages = "422-434" } @article{czo1994, author = "T. F. Xhan and J. Zou", title = "Additive {S}chwarz domain decomposition methods for elliptic problems on unstructured meshes", journal = NUMALGO, volume = "8", number = "2", year = "1994", pages = "329-346", note = "Errata, Numer. Algorithms, v9 n2, (1995), p.~397" } @techreport{cpv1991, author = "T. F. Chan and L. {De Pillis} and H. van der Vorst", title = " A transpose-free squared {L}anczos algorithm and application to solving nonsymmetric linear systems", number = "91-17 CAM", institution = "Dpt. of Mathematics, UCLA", year = "1991" } @article{cpv1998, author = "T. F. Chan and L. {De Pillis} and H. van der Vorst", title = "Transpose-free formulations of {L}anczos-type methods for nonsymmetric linear systems", journal = NUMALGO, volume = "17", number = "1", year = "1998", pages = "51-66" } @misc{cgz1997, author = "T. F. Chan and S. Go and L. Zikatanov", title = "Lecture notes on multilevel methods for elliptic problems on unstructured grids", howpublished = "Department of Mathematics, University of California, Los Angeles", year = "1997" } @article{cjz1983, author = "T. F. Chan and K. R. Jackson and B. Zhu", title = "Alternating direction incomplete factorizations", journal = SINUM, volume = "20", number = "2", year = "1983", pages = "239-257" } @article{ctw1997, author = "T. F. Chan and W. P. Tang and W. L. Wan", title = "Wavelet sparse approximate inverse preconditioners", journal = BITNM, volume = "37", number = "3", year = "1997", pages = "644-660" } @book{cgl2007, author = "R. H. Chan and C. Greif and D. P. {O'~Leary}", title = "Milestones in Matrix Computation: The Selected Works of {Gene H. Golub} with Commentaries", publisher = "Oxford University Press", address = "Oxford", year = "2007" } @article{cg1980, author = "W. M. Chan and A. George", title = "A linear time implementation of the {Reverse Cuthill-McKee} algorithm", journal = BITNM, volume = "20", number = "1", year = "1980", pages = "8-14" } @phdthesis{ch1978, author = "R. Chandra", title = "Conjugate gradient methods for partial differential equations", school = "Yale University", year = "1978" } @inproceedings{ces1975, author = "R. Chandra and S. C. Eisenstat and M. H. Schultz", title = "Conjugate gradient methods for partial differential equations", booktitle = "Computer Methods for Partial Differential Equations", editor = "R. Vichnevetsky", publisher = "AICA", year = "1975", pages = "60-64" } @article{cip1995, author = "S. Chandrasekaran and I. C. F. Ipsen", title = "On the sensitivity of solution components in linear systems of equations", journal = SIMAX, volume = "16", number = "1", year = "1995", pages = "93-112" } @article{cs1997, author = "A. Chapman and Y. Saad", title = "Deflated and augmented {K}rylov subspace techniques", journal = NLAA, volume = "4", year = "1997", pages = "43-66" } @article{csw2000, author = "A. Chapman and Y. Saad and L. Wigton", title = "High order {ILU} preconditioners for {CFD} problems", journal = "Int. J. Numer. Methods Fluids", volume = "33", number = "6", year = "2000", pages = "767-788" } @article{cro1989, author = "P. Charrier and J. Roman", title = "Algorithmique et calculs de complexit{\'e} pour un solveur de type dissection embo{\^\i}t{\'e}e", journal = NUMAT, volume = "55", year = "1989", pages = "463-476" } @techreport{cro1991, author = "P. Charrier and J. Roman", title = "Analysis of refined partitions for a parallel implementation of nested dissection", institution = "Universit{\'e} de Bordeaux, Laboratoire Bordelais de Recherche en Informatique", number = "LABRI 91-38", year = "1991" } @article{chm1982, author = "F. Chatelin and W. L. Miranker", title = "Acceleration by aggregation of successive approximation methods", journal = LAA, volume = "43", year = "1982", pages = "17-47" } @article{cks1978, author = "S. C. Chen and D. J. Kuck and A. H. Sameh", title = "Practical parallel band triangular system solvers", journal = TOMS, volume = "1", number = "3", year = "1978", pages = "270-277" } @article{cdh1984, author = "S. S. Chen and J. J. Dongarra and C. C. Hsiung", title = "Multiprocessing linear algebra algorithms on the {CRAY X-MP-2}: experiences with small granularity", journal = "J. Par. Dist. Comp.", volume = "1", year = "1984", pages = "22-31" } @article{cte1991, author = "T. Chen and R. Temam", title = "Incremental unknowns for solving partial differential equations", journal = NUMAT, volume = "59", year = "1991", pages = "255-271" } @techreport{cel1993, author = "M. P. Chernesky and H. C. Elman", title = "Costs of solving the discrete convection diffusion equation by relaxation methods", institution = "Computer Science Dept., University of Maryland", number = "CS-TR-3028", year = "1993" } @article{cel1993b, author = "M. P. Chernesky and H. C. Elman", title = "Ordering effects on relaxation methods applied to the discrete one-dimensional convection-diffusion equation", journal = SINUM, volume = "30", number = "5", year = "1993", pages = "1268-1290" } @article{chma1988, author = "R. C. Y. Chin and T. A. Manteuffel", title = "An analysis of block successive over-relaxation for a class of matrices with complex spectra", journal = SINUM, volume = "25", number = "3", year = "1988", pages = "564-585" } @inproceedings{chpw1992, author = "J. Choi and J. J. Dongarra and R. Pozo and D. W. Walker", title = "{ScaLAPACK: A} scalable linear algebra library for distributed memory concurrent computers", booktitle = "The Fourth Symposium on the Frontiers of Massively Parallel Computation", publisher = "IEEE", year = "1992", pages = "120-127" } @techreport{chs1994, author = "E. Chow and Y. Saad", title = "Approximate inverse preconditioners for general sparse matrices", institution = "Supercomputer Institute, University of Minnesota", number = "UMSI 94-101", year = "1994" } @article{chs1997, author = "E. Chow and Y. Saad", title = "Approximate inverse techniques for block-partitioned matrices", journal = SISC, volume = "18", number = "6", year = "1997", pages = "1657-1675" } @phdthesis{chro1987, author = "A. T. Chronopoulos", title = "A class of parallel iterative methods implemented on multiprocessors", school = "University of Illinois at Urbana-Champaign", year = "1987" } @article{ch1991, author = "A. T. Chronopoulos", title = "S-step iterative methods for (non)symmetric indefinite linear systems", journal = SINUM, volume = "28", number = "6", year = "1991", pages = "1776-1789" } @techreport{ch1990, author = "A. T. Chronopoulos", title = "Krylov subspace iterative methods for nonsymmetric indefinite linear systems", institution = "Computer Science Dept., University of Minnesota", number = "TR 90-21", year = "1990" } @article{chg1989b, author = "A. T. Chronopoulos and C. W. Gear", title = "On the efficient implementation of preconditioned s-step conjugate gradient methods on multiprocessors with memory hierarchy", journal = PARCOMP, volume = "11", number = "1", year = "1989", pages = "37-53" } @article{cfg1995, author = "M. T. Chu and R. E. Funderlic and G. H. Golub", title = "A rank one reduction formula and its applications to matrix factorizations", journal = SIREV, volume = "37", year = "1995", pages = "512-530" } @article{chg1987, author = "E. Chu and A. George", title = "Gaussian elimination with partial pivoting and load balancing on a multiprocessor", journal = PARCOMP, volume = "5", year = "1987", pages = "65-74" } @phdthesis{cia1992, author = "P. {Ciarlet Jr.}", title = "Etude de pr{\'e}conditionnements parall{\`e}les pour la r{\'e}solution d'{\'e}quations aux d{\'e}riv{\'e}es partielles elliptiques", school = "Universit{\'e} Paris 6", year = "1992" } @article{cia1994c, author = "P. {Ciarlet Jr.}", title = "Implementation of a domain decomposition method well suited for (massively) parallel architectures", journal = IJHSC, volume = "6", year = "1994", pages = "157-182" } @inproceedings{cia1994b, author = "P. {Ciarlet Jr.}", title = "A comparison of three iterative algorithms based on domain decomposition methods", booktitle = "Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition", editor = "D. E. Keyes and J. Xu", publisher = "American Mathematical Society", year = "1994", pages = "387-393" } @article{cia1994, author = "P. {Ciarlet Jr.}", title = "Repeated {Red-Black} ordering: a new approach", journal = NUMALGO, volume = "7", year = "1994", pages = "295-324" } @techreport{cil1994, author = "P. {Ciarlet Jr.} and F. Lamour", title = "An efficient low cost greedy graph partitioning heuristic", institution = "Dept. of Mathematics, UCLA", number = "CAM 94-1", year = "1994" } @techreport{cil1994b, author = "P. {Ciarlet Jr.} and F. Lamour", title = "Spectral partitioning methods and greedy partitioning methods: a comparison on finite element graphs", institution = "Dept. of Mathematics, UCLA", number = "CAM 94-9", year = "1994" } @article{cil1996, author = "P. {Ciarlet Jr.} and F. Lamour", title = "On the validity of a front oriented approach to partitioning large sparse graphs with a connectivity constraint", journal = NUMALGO, volume = "12", number = "1", year = "1996", pages = "193-214" } @article{cil1996b, author = "P. {Ciarlet Jr.} and F. Lamour", title = "Does contraction preserve triangular meshes?", journal = NUMALGO, volume = "13", number = "3-4", year = "1996", pages = "201-223" } @inproceedings{cils1995, author = "P. {Ciarlet Jr.} and F. Lamour and B. F. Smith", title = "On the influence of partitioning schemes on the efficiency of overlapping domain decomposition methods", booktitle = "Proceedings of the 5th Symposium on the Frontiers of Massively Parallel Computation", publisher = "IEEE", year = "1995", pages = "375–383" } @inproceedings{cim1994, author = "P. {Ciarlet Jr.} and G. Meurant", title = "A class of domain decomposition preconditioners for massively parallel computers", booktitle = "Proceedings of the Sixth International Conference on Domain Decomposition", editor = "A. Quarteroni and J. Périaux and Y. A. Kuznetsov and O. B. Widlund", publisher = "American Mathematical Society", year = "1994", pages = "353-360" } @techreport{cle1990, author = "A. Cleary", title = "Parallelism and fill-in in the {C}holesky factorization of reordered banded matrices", institution = "Sandia Nat. Lab.", number = "SAND90-2757", year = "1990" } @incollection{ccvl1982, author = "A. K. Cline and A. R. Conn and C. F. {Van Loan}", title = "Generalizing the {LINPACK} condition estimator", booktitle = "Lecture Notes in Mathematics 909", publisher = "Springer", year = "1982", pages = "73-83" } @article{cmsw1979, author = "A. K. Cline and C. B. Moler and G. W. Stewart and J. H. Wilkinson", title = "An estimate of the condition number of a matrix", journal = SINUM, volume = "16", year = "1979", pages = "368-375" } @article{ coh1974, author = "A. M. Cohen", title = "A note on pivot size in {G}aussian elimination", journal = LAA, volume = "8", year = "1974", pages = "361-368" } @article{cog1973, author = "P. Concus and G. H. Golub", title = "Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations", journal = SINUM, volume = "10", number = "6", year = "1973", pages = "1103-1120" } @inproceedings{cg1976, author = "P. Concus and G. H. Golub", title = "A generalized conjugate gradient method for nonsymmetric systems of linear equations", booktitle = "Computing Methods in Applied Sciences and Engineering", publisher = "Springer", address = "Berlin, Heidelberg", year ="1976", pages = "56-65" } @article{cgm1985, author = "P. Concus and G.H. Golub and G. Meurant", title = "Block preconditioning for the conjugate gradient method", journal = SISSC, volume = "6", year = "1985", pages = "220-252" } @inproceedings{cgol1976, author = "P. Concus and G. H. Golub and D. P. {O{'}Leary}", title = "A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = "Academic Press", year = "1976", pages = "309-332" } @article{com1986, author = "P. Concus and G. Meurant", title = "On computing {INV} block preconditionings for the conjugate gradient method", journal = BIT, volume = "26", year = "1986", pages = "493-504" } @inproceedings{coy1990, author = "J. W. Cooley", title = "How the {FFT} gained acceptance", booktitle = "A History of Scientific Computing", editor = "S. G. Nash", publisher = "ACM Press", year = "1990", pages = "133-140" } @article{cotu1965, author = "J. W. Cooley and J. W. Tukey", title = "An algorithm for the machine calculation of complex {F}ourier series", journal = MATCOMP, volume = "19,", number = "90", year = "1965", pages = "297-301" } @article{cdg1992, author = "J. D. F. Cosgrove and J. C. Diaz and A. Griewank", title = "Approximate inverse preconditionings for sparse linear systems", journal = "Int. J. Comput. Math.", volume = "44", number = "1-4", year = "1992", pages = "91-110" } @book{crqt1986, author = "M. Cosnard and Y. Robert and P. Quinton and M. Tchuente", title = "Parallel Algorithms and Architectures", publisher = "North-Holland", year = "1986" } @article{crt1986, author = "M. Cosnard and Y. Robert and D. Trystram", title = "Résolution parallèle de systèmes linéaires denses par diagonalisation", journal = "EDF, Bulletin DER, serie C", volume = "2", year = "1986", pages = "67-88" } @article{cot1974, author = "R. W. Cottle", title = "Manifestations of the {S}chur complement", journal = LAA, volume = "8", number = "3", year = "1974", pages = "189-211" } @phdthesis{cro1994, author = "L. Crouzet", title = "Résolution des équations de {M}axwell tridimensionnelles en régime fréquentiel par élements finis conformes, multiplicateurs de {L}agrange et méthodes itératives", school = "Université Paris 6", year = "1994" } @inproceedings{crm1994, author = "L. Crouzet and G. Meurant", title = "Solving the {3D} time harmonic {M}axwell equations with finite elements, {L}agrange multipliers and iterative methods", booktitle = "Finite Element Methods: Fifty Years of the {C}ourant Element", editor = "M. K\v{r}{\'{\i}}\v{z}ek and P. Neittaanm{\"{a}}ki and R. Stenberg", publisher = "CRC Press", year = "1994", pages = "173-182" } @article{cry1968, author = "C. W. Cryer", title = "Pivot growth in {G}aussian elimination", journal = NUMAT, volume = "12", year = "1968", pages = "335-345" } @article{csk1976, author = "L. Csanky", title = "Fast parallel matrix inversion algorithms", journal = SIC, volume = "5", number = "4", year = "1976", pages = "618-623" } @article{csv1984, author = "G. Csordas and R. S. Varga", title = "Comparisons of regular splittings of matrices", journal = NUMAT, volume = "44", year = "1984", pages = "23-35" } @techreport{cw1977, author = "J. K. Cullum and R. A. Willoughby", title = "The equivalence of the {L}anczos and the conjugate gradient algorithms", institution = "IBM Research Division", number = "RC 6903", year = "1977" } @article{cw1980, author = "J. K. Cullum and R. A. Willoughby", title = "The {L}anczos phenomenon - An iterpretation based upon conjugate gradient optimization", journal = LAA, volume = "29", year = "1980", pages = " " } @book{cw1985, author = "J. K. Cullum and R. A. Willoughby", title = "Lanczos Algorithms for Large Symmetric Eigenvalue Computations, {V}olume 1: {T}heory", publisher = "Birkhauser", year = "1985" } @book{cw1985b, author = "J. K. Cullum and R. A. Willoughby", title = "Lanczos Algorithms for Large Symmetric Eigenvalue Computations, {V}olume 2: {P}rograms", publisher = "Birkhauser", year = "1985" } @article{cre1971, author = "A. R. Curtis and J. K. Reid", title = "The solution of large sparse unsymmetric systems of linear equations", journal = IMAJ, volume = "8", number = "3", year = "1971", pages = "344-353" } @article{cre1972, author = "A. R. Curtis and J. K. Reid", title = "On the automatic scaling of matrices for {G}aussian elimination", journal = IMAJ, volume = "10", number = "l", year = "1972", pages = "118-124" } @inproceedings{cu1972, author = "E. H. Cuthill", title = "Several strategies for reducing the bandwidth of matrices", booktitle = "Sparse Matrices and their Applications", editor = "D. J. Rose and R. A. Willoughby", publisher = "Plenum Press", address = "New York", year = "1972", pages = "157-166" } @article{dah1983, author = "G. Dahlquist", title = "On matrix majorants and minorants with applications to differential equations", journal = LAA, volume = "52", year = "1983", pages = "199-216" } @article{dah1993, author = "G. Dahlquist", title = "A ``multigrid'' extension of the {FFT} for the numerical inversion of {F}ourier and {L}aplace transforms", journal = BIT, volume = "33", year = "1993", pages = "85-112" } @book{db1974, author = "G. Dahlquist and \AA. Bj{\"{o}}rck", title = "Numerical Methods", publisher = "Prentice-Hall", year = "1974" } @article{deg1972, author = "G. Dahlquist and S. C. Eisenstat and G. H. Golub", title = "Bounds for the error of linear systems of equations using the theory of moments", journal = JMAA, volume = "37", year = "1972", pages = "151-166" } @article{dak1992, author = "W. Dahmen and A. Kunoth", title = "Multilevel preconditioning", journal = NUMAT, volume = "63", year = "1992", pages = "315-344" } @book{dau1992, author = "I. Daubechies", title = "Ten Lectures on Wavelets", publisher = "SIAM", year = "1992", note = "CBMS–NSF Regional Conference Series in Applied Mathematics, 61" } @book{dal1985, author = "R. Dautray and J. L. Lions", title = "Analyse Mathématique et Calcul Numérique pour les Sciences et Techniques", publisher = "Masson", year = "1985" } @article{dad1987, author = "A. K. Dave and I. S. Duff", title = "Sparse matrix calculations on the {C}ray 2", journal = PARCOMP, volume = "5", year = "1987", pages = "55-64" } @book{pra1984, author = "P. J. Davis and P. Rabinowitz", title = "Methods of Numerical Integration", publisher = "Academic Press", year = "1984" } @techreport{dav1992, author = "T. A. Davis", title = "Performance of an unsymmetric pattern multifrontal method for sparse {LU} factorization", institution = "University of Florida", number = "TR-92-014", year = "1992" } @techreport{dav1993, author = "T. A. Davis", title = "Users' guide for the unsymmetric pattern multifrontal package", institution = "University of Florida", number = "TR-93-020", year = "1993" } @techreport{dav1994, author = "T. A. Davis", title = "A combined unifrontal/multifrontal method for unsymmetric sparse matrices", institution = "University of Florida", number = "TR-94-005", year = "1994" } @article{dd1997, author = "T. A. Davis and I. S. Duff", title = "An unsymmetric{-}pattern multifrontal method for sparse {LU} factorization", journal = SIMAX, volume = "18", number = "1", year = "1997", pages = "140-158" } @article{day1990, author = "T. A. Davis and P. C. Yew", title = "A nondeterministic parallel algorithm for unsymmetric sparse {LU} factorization", journal = SIMAX, volume = "11", year = "1990", pages = "383-402" } @article{ddd1991, author = "C. N. Dawson and Q. Du and T. F. Dupont", title = "A finite difference domain decomposition algorithm for numerical solution of the heat equation", journal = MATCOMP, volume = "57", number = "195", year = "1991", pages = "63-71" } @article{dwd1992, author = "C. N. Dawson and T. F. Dupont", title = "Explicit/implicit conservative {G}alerkin domain decomposition procedures for parabolic problems", journal = MATCOMP, volume = "58", number = "197", year = "1992", pages = "21-34" } @article{dwd1994, author = "C. N. Dawson and T. F. Dupont", title = "Explicit/implicit, conservative domain decomposition procedures for parabolic problems based on block-centered finite differences", journal = SINUM, volume = "31", year = "1994", pages = "1045-1061" } @phdthesis{day1993, author = "D. Day", title = "Semi-duality in the two-sided {L}anczos algorithm", school = "University of California, Berkeley", year = "1993" } @article{ddu1989, author = "M. J. Daydé and I. S. Duff", title = "Use of {Level 3 BLAS} in {LU} factorization on the {Cray 2, the ETA-10P and the IBM 3090/VF}", journal = IJSA, volume = "3", number = "2", year = "1989", pages = "40-70" } @article{ddp1994, author = "M. J. Daydé and I. S. Duff and A. Petitet", title = "A parallel block implementation of level-3 {BLAS} for {MIMD} vector processors", journal = TOMS, volume = "20", number = "2", year = "1994", pages = "178-193" } @techreport{daer1999, author = "E. F. {D'Azevedo} and V. Eijkhout and C. H. Romine", title = "Conjugate gradient algorithms with reduced synchronization overhead on distributed memory multiprocessors", institution = "University of Tennessee", number = "Lapack Working Notes 56", year = "1999" } @article{dft1992, author = "E. F. {D'Azevedo} and P. A. Forsyth and W.-P. Tang", title = "Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems", journal = SIMAX, volume = "13", number = "3", year = "1992", pages = "944-961" } @article{dft1992b, author = "E. F. {D'Azevedo} and P. A. Forsyth and W.-P. Tang", title = "Towards a cost-effective {ILU} preconditioner with high level fill", journal = BITNM, volume = "32", number = "3", year = "1992", pages = "442-463" } @article{dbr1982, author = "C. {de Boor} and J. R. Rice", title = "Extremal polynomials with application to {R}ichardson iteration for indefinite linear systems", journal = SISSC, volume = "3", number = "1", year = "1982", pages = "47-57" } @article{dko1977, author = "S. Demko", title = "Inverses of band matrices and local convergence of spline projections", journal = SINUM, volume = "14", year = "1977", pages = "616-619" } @article{dms1984, author = "S. Demko and W. F. Moss and P. W. Smith", title = "Decay rates for inverses of band matrices", journal = MATCOMP, volume = "43", number = "168", year = "1984", pages = "491-499" } @incollection{dem1982, author = "J. W. Demmel", title = "The condition number of equivalence transformations that block diagonalize matrix pencils", booktitle = "Matrix Pencils", editor = "B. K{{\aa}}gstr{\"{o}}m and A. Ruhe", note = "Lecture Notes in Mathematics 973", year = "1982", publisher = "Springer", pages = "2-16" } @article{dem1984, author = "J. W. Demmel", title = "Underflow and the reliability of numerical software", journal = SISSC, volume = "5", year = "1984", pages = "887-919" } @article{dem1987, author = "J. W. Demmel", title = "On condition numbers and the distance to the nearest ill-posed problem", journal = NUMAT, volume = "51", number = "3", year = "1987", pages = "251-289" } @techreport{dem1989, author = "J. W. Demmel", title = "On floating point errors in {C}holesky", institution = "University of Tennessee", number = "Lapack Working note 14", year = "1989" } @techreport{dem1992, author = "J. W. Demmel", title = "Open problems in numerical linear algebra", institution = "University of Minnesota", number = "CS-92-164", year = "1992" } @techreport{dem1992b, author = "J. W. Demmel", title = "Trading off parallelism and numerical stability", institution = "University of California, Berkeley", number = "UCB/CSD-92-702", year = "1992" } @article{dem1992c, author = "J. W. Demmel", title = "The componentwise distance to the nearest singular matrix", journal = SIMAX, volume = "13", number = "1", year = "1992", pages = "10-19" } @book{dem1997, author = "J. W. Demmel", title = "Applied Numerical Linear Algebra", publisher = "SIAM", year = "1997" } @article{dgl1999, author = "J. W. Demmel and J. R. Gilbert and X. S. Li", title = "An asynchronous parallel supernodal algorithm for sparse {G}aussian elimination", journal = SIMAX, volume = "20", number = "4", year = "1999", pages = "915-952" } @article{dhvdv1993, author = "J. W. Demmel and M. T. heath and H. A. {van der Vorst}", title = "Parallel numerical linear algebra", journal = ACTNUM, volume = "2", year = "1993", pages = "111-197" } @article{dhs1995, author = "J. W. Demmel and N. J. Higham and R. S. Schreiber", title = "Stability of block {LU} factorization", journal = NLAA, volume = "2", number = "2", year = "1995", pages = "173-190" } @article{den1982, author = "J. E. Dendy", title = "Black box multigrid", journal = JCP, volume = "48", year = "1982", pages = "366-386" } @inproceedings{dhy1981, author = "J. E. Dendy and J. M. Hyman", title = "Multigrid and {ICCG} for problems with interfaces", booktitle = "Elliptic Problem Solvers", editor = "M. H. Schultz", publisher = "Academic Press", year = "1981", pages = "247-253" } @article{dta1995, author = "J. E. Dendy and C. C. Tazartes", title = "Grandchild of the frequency decomposition multigrid method", journal = SISC, volume = "16", year = "1995", pages = "307–319" } @article{dtu1987, author = "J. E. {Dennis Jr.} and K. Turner", title = "Generalized conjugate directions", journal = LAA, volume = "88", year = "1987", pages = "187-209" } @article{dpil1978, author = "J. {De Pillis}", title = "Faster convergence for iterative solutions to systems via three-part splittings", journal = SINUM, volume = "15", number = "5", year = "1978", pages = "888-911" } @article{dpn1981, author = "J. {De Pillis} and M. Neumann", title = "Iterative methods with k-part splittings", journal = IMAJNA, volume = "1", year = "1981", pages = "65-79" } @techreport{dgms1996, author = "V. R. Deshpande and M. J. Grote and P. Messmer and W. B. Sawyer", title = "Parallel sparse approximate inverse preconditioner", institution = "Swiss Center for Scientific Computing", number = "TR-96-14", year = "1996" } @techreport{dtd1994, author = "F. Desprez and B. Tourancheau and J. J. Dongarra", title = "Performance complexity of {LU} factorization with efficient pipelining and overlap on a multiprocessor", institution = "University of Tennessee", number = "Lapack Working Note 67", year = "1994", pages = " " } @article{dst1996, author = "E. {de Sturler}", title = "Nested {K}rylov methods based on {GCR}", journal = JCAM, volume = "67", year = "1996", pages = "15-41" } @article{dst1996b, author = "E. {de Sturler}", title = "A performance model for {K}rylov subspace methods on mesh-based parallel computers", journal = PARCOMP, volume = "22", number = "1", year = "1996", pages = "57-74" } @inproceedings{dst1994, author = "E. {de Sturler}", title = "{IBLU} preconditioners for massively parallel computers", booktitle = "Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition", editor = "D. E. Keyes and J. Xu", publisher = "American Mathematical Society", year = "1994", pages = "395-400" } @inproceedings{dsf1993, author = "E. {de Sturler} and D. R. Fokkema", title = "Nested {K}rylov methods and preserving the orthogonality", booktitle = "Sixth Copper Mountain Conference on Multigrid Methods", editor = "D. Melson and T. Manteuffel and S. F. {Mc Cormick}", publisher = "NASA conference publication 3324", year = "1993", pages = "111-126" } @article{dsv1995, author = "E. {de Sturler} and H. A. van der Vorst", title = "Reducing the effect of global communication in {GMRES}(m) and {CG} on parallel distributed memory computers", journal = ANM, volume = "18", number = "4", year = "1995", pages = "441-459" } @article{dif1976, author = "M. A. Diamond and D. L. V. Ferreira", title = "On a cyclic reduction method for the solution of {P}oisson's equation", journal = SINUM, volume = "13", number = "1", year = "1976", pages = "54-70" } @inproceedings{dghkpp1992, author = "Q. V. Dinh and R. Glowinski and J. He and V. Kwock and T. W. Pan and J. Périaux", title = "Lagrange multiplier approach to fictitious domain methods: application to fluid dynamics and electro-magnetics", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "151-194" } @inproceedings{dgp1980, author = "Q. V. Dinh and R. Glowinski and J. Périaux", title = "Résolution numérique des équations de {Navier-Stokes} par des méthodes de décomposition de domaines", booktitle = "Méthodes Numériques dans les Sciences de l'Ingénieur", editor = "E. Absi and R. Glowinski and P. Lascaux and H. Veysseyre", publisher = "Dunod", year = "1980", pages = "383-404" } @inproceedings{dgpt1988, author = "Q. V. Dinh and R. Glowinski and J. Périaux and G. Terrasson", title = "On the coupling of viscous and inviscid models for incompressible fluid flows via domain decomposition", booktitle = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and G. H. Golub and G. Meurant and J. Périaux", publisher = "SIAM", year = "1988", pages = "350-369" } @article{doi1991, author = "S. Doi", title = "On parallelism and convergence of incomplete {LU} factorizations", journal = ANM, volume = "7", number = "5", year = "1991", pages = "417-436" } @inproceedings{doi1991b, author = "S. Doi", title = "A {G}ustafsson-type modification for parallel ordered incomplete {LU} factorizations", booktitle = "Advances in Numerical Methods for Large Sets of Linear Systems", editor = "T. Nodera", publisher = "Keio University", year = "1991", pages = "?-?" } @article{doh1992, author = "S. Doi and A. Hoshi", title = "Large-numbered multicolor {MILU} preconditioning on {SX-3/14}", journal = "Intl. J. Comput. Math.", volume = "44", number = "1-4", year = "1992", pages = "143-152" } @article{dol1990, author = "S. Doi and A. Lichnewsky", title = "Some parallel and vector implementations of preconditioned iterative methods on {C}ray-2", journal = IJHSC, volume = "2", number = "02", year = "1990", pages = "143-179" } @techreport{dol1991, author = "S. Doi and A. Lichnewsky", title = "A graph-theory approach for analyzing the effects of ordering on {ILU} preconditionning", institution = "INRIA", address = "Rocquencourt, France", number = "RR-1452", year = "1991" } @phdthesis{don1991, author = "J. M. Donato", title = "Iterative methods for scalar and coupled systems of elliptic equations", school = "Dept. of Mathematics, UCLA", year = "1991" } @article{doc1992, author = "J. M. Donato and T. F. Chan", title = "Fourier analysis of incomplete factorization preconditioners for {3D} anisotropic problems", journal = SISSC, volume = "13", number = "1", year = "1992", pages = "319-338" } @article{dod1991, author = "J. J. Dongarra and J. W. Demmel", title = "{LAPACK}: a portable high-performance numerical library for linear algebra", journal = "Supercomputer", volume = "46", year = "1991", pages = "33-38" } @book{ddgm1989, author = "J. J. Dongarra and I. S. Duff and P. Gaffney and S. McKee Eds.", title = "Vector and Parallel Computing, Issues in Applied Research and Development", publisher = "Ellis Horwood", year = "1989" } @book{ddsvdv1991, author = "J. J. Dongarra and I. S. Duff and D. C. Sorensen and H. A. {van der Vorst}", title = "Solving Linear Systems on Vector and Shared Memory Computers", publisher = "SIAM", year = "1991" } @article{dgk1984, author = "J. J. Dongarra and F. G. Gustavson and A. Karp", title = "Implementing linear algebra algorithms for dense matrices on a vector pipeline machine", journal = SIREV, volume = "26", number = "1", year = "1984", pages = "91-112" } @article{doh1986, author = "J. J. Dongarra and T. Hewitt", title = "Implementing dense linear algebra algorithms using multitasking on the Cray {X–MP–4} (or approaching the {G}igaflop)", journal = SISSC, volume = "7", number = "1", year = "1986", pages = "347-305" } @article{dos1984, author = "J. J. Dongarra and A. H. Sameh", title = "On some parallel banded system solvers", journal = PARCOMP, volume = "1", year = "1984", pages = "223-235" } @article{doe1984, author = "J. J. Dongarra and S. C. Eisenstat", title = "Squeezing the most out of an algorithm in {CRAY FORTRAN}", journal = TOMS, volume = "10", number = "3", year = "1984", pages = "219-230" } @book{dbms1979, author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart", title = "Linpack User{'}s Guide", publisher = "SIAM", address = "Philadelphia", year = "1979" } @article{ddhh1988, author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and R. J. Hanson", title = "An extended set of {FORTRAN} basic linear algebra subprograms", journal = TOMS, volume = "14", number ="1", year = "1988", pages = "1-17" } @article{ddhd1990, author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and I. S. Duff", title = "Algorithm 679: {A} set of level 3 basic linear algebra subprograms: model implementation and test programs", journal = TOMS, volume = "16", number ="1", year = "1990", pages = "18-28" } @techreport{dow1993, author = "J. J. Dongarra and D. W. Walker", title = "The design of linear algebra libraries for high performance computers", institution = "Oak Ridge National Lab.", number = "ORNL/TM-12404", year = "1993" } @article{drr1970, author = "F. W. Dorr", title = "The direct solution of the discrete {P}oisson equation on a rectangle", journal = SIREV, volume = "12", number = "2", year = "1970", pages = "248-263" } @article{drr1975, author = "F. W. Dorr", title = "The direct solution of the discrete {P}oisson equation in {O}($n^2$) operations", journal = SIREV, volume = "17", number = "3", year = "1975", pages = "412-415" } @article{dou1984, author = "C. C. Douglas", title = "Multi-grid algorithms with applications to elliptic boundary-value problems", journal = SINUM, volume = "21", number = "2", year = "1984", pages = "236-254" } @inproceedings{dou1990, author = "C. C. Douglas", title = "A variation of the {S}chwarz alternating method: the domain decomposition reduction method", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1990", pages = "191-201" } @article{dou1994, author = "C. C. Douglas", title = "Some remarks on completely vectorizing point {Gauss–Seidel} while using the natural ordering", journal = "Advances Comput. Math.", volume = "2", year = "1994", pages = "215-222" } @inproceedings{dou1996, author = "C. C. Douglas", title = "A review of numerous parallel multigrid methods", booktitle = "Applications on Advanced Architecture Computers", editor = "G. Astfalk", publisher = "SIAM", year ="1996", pages = "187-202" } @article{dou1993, author = "C. C. Douglas and J. {Douglas, Jr.}", title = "A unified convergence theory for abstract multigrid or multilevel algorithms, serial and parallel", journal = SINUM, volume = "30", year = "1993", pages = "136-158" } @article{ddf1994, author = "C. C. Douglas and J. Douglas and D. E. Fyfe", title = "A multigrid unified theory for non-nested grids and/or quadrature", journal = "East-West J. Numer. Math.", volume = "2", year = "194", pages = "285-294" } @misc{dms1997, author = "C. C. Douglas and M. Malhotra and M. H. Schultz", title = "Parallel multigrid with {AD}-like smoothers in two dimensions", howpublished = "Report available in MGNET", year = "1997" } @book{dra1983, author = "A. Draux", title = "Polyn{\^o}mes Orthogonaux Formels. Applications", volume = "LNM 974", publisher = "Springer-Verlag", year = "1983" } @article{dtt1998, author = "T. A. Driscoll and K.-C. Toh and L. N. Trefethen", title = "From potential theory to matrix iterations in six steps", journal = SIREV, volume = "40", number = "3", year = "1998", pages = "547-578" } @article{dgrs1995, author = "J. Drko\v{s}ov{\`a} and A. Greenbaum and M. Rozlo\v{z}n\'{\i}k and Z. Strako\v{s}", title = "Numerical stability of {GMRES}", journal = BITNM, volume = "35", number = "3", year = "1995", pages = "309-330" } @article{dov1994, author = "Z. Drma\v{c} and M. Omladi\v{c} and K. Veseli\v{c}", title = "On the perturbation of the {C}holesky factorization", journal = SIMAX, volume = "15", number = "4", year = "1994", pages = "1319-1332" } @article{dry1993, author = "M. Dryja", title = "A finite element capacitance matrix method for the elliptic problem", journal = SINUM, volume = "20", number = "4", year = "1993", pages = "671-680" } @article{drp1985, author = "M. Dryja and W. Proskurowski", title = "Capacitance matrix method using strips with alternating {N}eumann and {D}irichlet boundary conditions", journal = ANM, volume = "1", year = "1985", pages = "285-298" } @inproceedings{dpw1987, author = "M. Dryja and W. Proskurowski and O. B.Widlund", title = "Numerical experiments and implementation of a domain decomposition method with crosspoints for the model problem", booktitle = "Advances in Computer Methods for Partial Differential Equations - {VI}", editor = "R. Vichnevetsky and R. S. Stepleman", publisher = "IMACS", year = "1987", pages = "22-27" } @inproceedings{dpw1986, author = "M. Dryja and W. Proskurowski and O. B.Widlund", title = "Method of domain decomposition with cross points for elliptic finite element problems", booktitle = "Proceedings of the International Symposium on Optimal Algorithm", editor = "B. Sendov", publisher = "Bulgarian Academy of Sciences", year = "1986", pages = "97-111" } @article{dsw1994, author = "M. Dryja and B. F. Smith and O. B. Widlund", title = "Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions", journal = SINUM, volume = "31", number = "6", year = "1994", pages = "1662-1694" } @inproceedings{drw1990, author = "M. Dryja and O. B. Widlund", title = "Towards a unified theory of domain decomposition algorithms for elliptic problems", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1990", pages = "3-21" } @inproceedings{drw1992, author = "M. Dryja and O. B. Widlund", title = "Additive {S}chwarz methods for elliptic finite element problems in three dimensions", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "3-18" } @article{drw1994, author = "M. Dryja and O. B. Widlund", title = "Domain decomposition algorithms with small overlap", journal = SISC, volume = "15", year = "1994", pages = "604-620" } @article{dsm1963, author = "E. {D'Sylva} and G. A. Miles", title = "The {SSOR} iteration scheme for equations with $\sigma_1$ ordering", journal = COMPJ, volume = "6", number = "4", year = "1963", pages = "366-367" } @article{dgr1979, author = "P. F. Dubois and A. Greenbaum and G. H. Rodrigue", title = "Approximating the inverse of a matrix for use in iterative algorithms on vector processors", journal = COMP, volume = "22", number = "3", year = "1979", pages = "257-268" } @article{dch1992, author = "J. J. {Du Croz} and N. J. Higham", title = "Stability of methods for matrix inversion", journal = JIMA, volume = "12", year = "1992", pages = "1–19" } @article{duf1974, author = "I. S. Duff", title = "On the number of nonzeros added when {G}aussian elimination is performed on sparse random matrices", journal = MATCOMP, volume = "28", number = "125", year = "1974", pages = "219-230" } @article{duf1977, author = "I. S. Duff", title = "A survey of sparse matrix research", journal = PIEEE, volume = "65", number = "4", year = "1977", pages = "500-535" } @book{duf1981b, author = "I. S. {Duff Ed.}", title = "Sparse Matrices and their Uses", publisher = "Academic Press", year = "1981", note = "Proceedings of the IMA Numerical Analysis Group Conference held at the University of Reading, 9th-11th July, 1980" } @techreport{duf1981c, author = "I. S. Duff", title = "MA32, a package for solving sparse unsymmetric systems using the frontal method", institution = "Harwell Laboratory", number = "AERE R10079", year = "1981" } @techreport{duf1983, author = "I. S. Duff", title = "The solution of sparse linear equations on the {C}ray 1", institution = "Harwell Laboratory", number = "CSS125", year = "1983" } @inproceedings{duf1984c, author = "I. S. Duff", title = "The solution of nearly symmetric sparse linear systems", booktitle = "Computing Methods in Applied Sciences and Engineering, VI", editor = "R. Glowinski and J.-L. Lions", publisher = "North-Holland", year = "1984", pages = "57-74" } @article{duf1984, author = "I. S. Duff", title = "Design features of a frontal code for solving sparse unsymmetric linear systems out-of-core", journal = SISSC, volume = "5", year = "1984", pages = "270-280" } @article{duf1984d, author = "I. S. Duff", title = "Direct methods for solving sparse systems of linear equations", journal = SISSC, volume = "5", number = "3", year = "1984", pages = "605-619" } @incollection{duf1985, author = "I. S. Duff", title = "Data structures, algorithms and software for sparse matrices", booktitle = "Sparsity and its Applications", editor = "D J. Evans", publisher = "Cambridge University Press", address = "Cambridge, U.K.", year = "1985", pages = "1-29" } @article{duf1986, author = "I. S. Duff", title = "Parallel implementation of multifrontal schemes", journal = PARCOMP, volume = "3", year = "1986", pages = "193-204" } @incollection{duf1987, author = "I. S. Duff", title = "The use of vector and parallel computers in the solution of large sparse linear equations", booktitle = "Large Scale Scientific Computing", editor = "P. Deuflhard and B. Engquist", publisher = "Birkh{\"{a}}user", year = "1987", pages = "331-348" } @inproceedings{duf1987b, author = "I. S. Duff", title = "The influence of vector and parallel processors on numerical analysis", booktitle = "State of the Art in Numerical Analysis", editor = "A. Iserles and M. J. D. Powell", publisher = "Clarendon Press", year = "1987", pages = "359-407" } @article{duf1988, author = "I. S. Duff", title = "Multiprocessing a sparse matrix code on the {Alliant FX/8}", journal = JCAM, volume = "27", number = "1-2", year = "1988", pages = "229-239" } @inproceedings{duf1993, author = "I. S. Duff", title = "The solution of augmented systems", booktitle = "Numerical analysis 1993", editor = " D. F. Griffiths and G. A. Watson", publisher = "Longman Scientific and Technical", year = "1984", pages = "40-55" } @techreport{dgl1987, author = "I. S. Duff and N. I. Gould and M. Lescrenier and J. K. Reid", title = "The multifrontal method in a parallel environment", institution = "Harwell Laboratory", number = "CSS 211", year = "1987" } @article{dgrst1990, author = "I. S. Duff and N. I. Gould and J. K. Reid and J. A. Scott and K. Turner", title = "The factorization of sparse symmetric indefinite matrices", journal = IMAJNA, volume = "11", number = "2", year = "1990", pages = "181-204" } @inproceedings{duj1989, author = "I. S. Duff and S. L. Johnson", title = "Node ordering and concurrency in structurally symmetric sparse problems", booktitle = "Parallel Supercomputing: Methods, Algorithms and Applications", editor = "G. F. Carey", publisher = "John Wiley and Sons", year = "1989", pages = "?-?" } @article{dllt1987, author = "I. S. Duff and J. Laminie and A. Lichnewsky and F. Thomasset", title = "An experiment with arithmetic precision in linear algebra computations", journal = "Int. J. Num. Meth. Fluids", volume = "7", number = "10", year = "1987", pages = "1077-1092" } @article{dm1989, author = "I. S. Duff and G. Meurant", title = "The effect of ordering on preconditioned conjugate gradients", journal = BIT, volume = "29", year = "1989", pages = "635-657" } @article{dr1974, author = "I. S. Duff and J. K. Reid", title = "A comparison of sparsity orderings for obtaining a pivotal sequence in {G}aussian elimination", journal = JIMA, volume = "14", year = "1974", pages = "281-291" } @article{dr1979, author = "I. S. Duff and J. K. Reid", title = "Some design features of a sparse matrix code", journal = TOMS, volume = "5", number = "1", year = "1979", pages = "18-35" } @article{dr1983, author = "I. S. Duff and J. K. Reid", title = "The multifrontal solution of indefinite sparse symmetric linear equations", journal = TOMS, volume = "9", number = "3", year = "1983", pages = "302-325" } @article{dr1984, author = "I. S. Duff and J. K. Reid", title = "The multifrontal solution of unsymmetric sets of linear equations", journal = SISSC, volume = "5", number = "3", year = "1984", pages = "633-641" } @techreport{dr1993, author = "I. S. Duff and J. K. Reid", title = "{MA48}, a {F}ortran code for direct solution of sparse unsymmetric linear systems of equations", institution = "Rutherford Appleton Laboratory", number = "RAL–93–072", year = "1993" } @techreport{dr1995, author = "I. S. Duff and J. K. Reid", title = "{MA47}, a {F}ortran code for direct solution of indefinite sparse symmetric linear systems", institution = "Rutherford Appleton Laboratory", number = "RAL–95–001", year = "1995" } @article{dr1996, author = "I. S. Duff and J. K. Reid", title = "The design of {MA48}: a code for the direct solution of sparse unsymmetric linear systems of equations", journal = TOMS, volume = "22", number = "2", year = "1996", pages = "187-226" } @article{der1976, author = "I. S. Duff and A. M. Erisman and J. K. Reid", title = "On {G}eorge's nested dissection method", journal = SINUM, volume = "13", number = "5", year = "1976", pages = "686-695" } @book{der2017, author = "I. S. Duff and A. M. Erisman and J. K. Reid", title = "Direct Methods for Sparse Matrices", edition = "2nd", publisher = "Oxford University Press", note = "First edition 1987", year = "2017" } @article{drs1989, author = "I. S. Duff and J. K. Reid and J. A. Scott", title = "The use of profile reduction algorithms with a frontal code", journal = IJNME, volume = "28", year = "1989", pages = "2555-2568" } @article{drmn1979, author = "I. S. Duff and J. K. Reid and N. Munksgaard and B. Nielsen", title = "Direct solution of sets of linear equations whose matrix is sparse, symmetric and indefinite", journal = JIMA, volume = "23", year = "1979", pages = "235-250" } @techreport{ds1993, author = "I. S. Duff and J. A. Scott", title = "{MA42}- {A} new frontal code for solving sparse unsymmetric systems", institution = "Rutherford Appleton Laboratory", number = "RAL-93-064", year = "1993" } @techreport{ds1994, author = "I. S. Duff and J. A. Scott", title = "The use of multiple fronts in {G}aussian elimination", institution = "Rutherford Appleton Laboratory", number = "RAL-94-040", year = "1994" } @book{ds1979, author = "I. S. Duff and G. W. Stewart", title = "Sparse Matrix Proceedings, 1978", publisher = "SIAM", year = "1979" } @article{dup1968, author = "T. F. Dupont", title = "A factorization procedure for the solution of elliptic difference equations", journal = SINUM, volume = "5", number = "4", year = "1968", pages = "753-782" } @incollection{dsr1970, author = "T. F. Dupont and H. L. Stone and H. H. Rachford", title = "Factorization techniques for elliptic difference equations", booktitle = "Studies in Numerical Analysis 2", publisher = "SIAM", year = "1970", pages = "168-174" } @article{dkr1968, author = "T. F. Dupont and R. P. Kendall and H. H. Rachford", title = "An approximate factorization procedure for solving self-adjoint elliptic difference equations", journal = SINUM, volume = "5", number = "3", year = "1968", pages = "559-573" } @article{ ede1993, author = "A. Edelman", title = "Large dense numerical linear algebra in 1993, the parallel computing influence", journal = IJSA, volume = "7", number = "2", year = "1993", pages = "113-128" } @article{ emt1998, author = "A. Edelman and P. McCorquodale and S. Toledo", title = "The future fast {F}ourier transform?", journal = SISC, volume = "20", number = "", year = "1998", pages = "1094-1114" } @misc{edo1991, author = "A. Edelman and M. Ohlroch", title = "Editor's Note", howpublished = "SIAM J. Matrix Anal. Appl., vol 12", year = "1991" } @article{erl1964, author = "L. W. Ehrlich", title = "The block symmetric successive overrelaxation method", journal = SIAMJ, volume = "12", number = "4", year = "1964", pages = "807-826" } @article{erl1971, author = "L. W. Ehrlich", title = "Solving the biharmonic equations as coupled finite difference equations", journal = SINUM, volume = "8", number = "2", year = "1971", pages = "278–287" } @article{erl1972, author = "L. W. Ehrlich", title = "Coupled harmonic equations, {SOR} and {C}hebyshev acceleration", journal = MATCOMP, volume = "26", number = "118", year = "1972", pages = "335-343" } @article{erl1979, author = "L. W. Ehrlich", title = "Solving the biharmonic equation on irregular regions", journal = TOMS, volume = "5", number = "3", year = "1979", pages = "251-258" } @article{ehg1975, author = "L. W. Ehrlich and M. M. Gupta", title = "Some difference schemes for the biharmonic equation", journal = SINUM, volume = "12", number = "5", year = "1975", pages = "773–790" } @article{en1983, author = "M. Eiermann and W. Niethammer", title = "On the construction of semiiterative methods", journal = SINUM, volume = "20", number = "6", year = "1983", pages = "1153-1160" } @article{env1985, author = "M. Eiermann and W. Niethammer and R. S. Varga", title = "A study of semiiterative methods for nonsymmetric systems of linear equations", journal = NUMAT, volume = "47", year = "1985", pages = "505-533" } @article{eij1988, author = "V. Eijkhout", title = "A general formulation for incomplete blockwise factorizations", journal = CANM, volume = "4", year = "1988", pages = "161–164" } @article{eij1991, author = "V. Eijkhout", title = "Analysis of parallel incomplete point factorizations", journal = LAA, volume = "154", year = "1991", pages = "723-740" } @techreport{eij1994, author = "V. Eijkhout", title = "Computational variants of the {CGS} and {BiCGstab} methods", number = "UT-CS-94-241", institution = "Dpt. of Computer Science, University of Tennessee", year = "1994" } @article{eip1988, author = "V. Eijkhout and B. Polman", title = "Decay rates of inverses of banded {M}-matrices that are near to {T}oeplitz matrices", journal = LAA, volume = "109", year = "1988", pages = "247-277" } @article{eiv1986, author = "V. Eijkhout and P. S. Vassilevski", title = "Positive definiteness aspects of vectorizable preconditioners", journal = PARCOMP, volume = "10", year = "1986", pages = "93–100" } @article{ei1981, author = "S. C. Eisenstat", title = "Efficient implementation of a class of preconditioned conjugate gradient methods", journal = SISSC, volume = "2", number = "1", year = "1981", pages = "1-4" } @article{eis1983, author = "S. C. Eisenstat", title = "A note on the generalized conjugate gradient method", journal = SINUM, volume = "20", number = "2", year = "1983", pages = "358-361" } @article{ees1983, author = "S. C. Eisenstat and H. C. Elman and M. H. Schultz", title = "Variational iterative methods for nonsymmetric systems of linear equations", journal = SINUM, volume = "20", year = "1983", pages = "345-367" } @inproceedings{ees1985, author = "S. C. Eisenstat and H. C. Elman and M. H. Schultz", title = "Block preconditioned conjugate gradient like methods for numerical reservoir simulation", booktitle = "SPE Reservoir Simulation Symposium Proceedings", year = "1985", pages = "397-405", note = "Paper SPE 13534" } @article{els1982, author = "S. C. Eisenstat and J. W. Lewis and M. H. Schultz", title = "Optimal block diagonal scaling of block 2-cyclic matrices", journal = LAA, volume = "44", year = "1982", pages = "181-186" } @article{ehhr1988, author = "S. C. Eisenstat and M. T. Heath and C. S. Henkel and C. H. Romine", title = "Modified cyclic algorithms for solving triangular systems on distributed memory multiprocessors", journal = SISSC, volume = "9", number = "3", year = "1988", pages = "589-600" } @inproceedings{ess1975, author = "S. C. Eisenstat and M. H. Schultz and A. H. Sherman", title = "Application of sparse matrix methods to partial differential equations", booktitle = "Advances in Computer Methods for Partial Differential Equations", editor = "R. Vichnevetsky", publisher = "IMACS", year = "1975", pages = "40-45" } @article{ess1981, author = "S. C. Eisenstat and M. H. Schultz and A. H. Sherman", title = "Algorithms and data structures for sparse symmetric {G}aussian elimination", journal = SISSC, volume = "2", year = "1981", pages = "225-237" } @article{elf1980, author = "T. Elfving", title = "Block-iterative methods for consistent and inconsistent linear equations", journal = NUMAT, volume = "35", year = "1980", pages = "1-12" } @article{el1986, author = "H. C. Elman", title = "A stability analysis of incomplete {LU} factorizations", journal = MATCOMP, volume = "47", number = "175", year = "1986", pages = "191-217" } @article{el1989, author = "H. C. Elman", title = "Approximate {S}chur complement preconditioners on serial and parallel computers", journal = SISSC, volume = "10", number = "3", year = "1989", pages = "581-605" } @article{el1989b, author = "H. C. Elman", title = "Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems", journal = BITNM, volume = "29", number = "4", year = "1989", pages = "890-915" } @article{el1996, author = "H. C. Elman", title = "Multigrid and {K}rylov subspace methods for the discrete {S}tokes equations", journal = "Int. J. Numer. Methods Fluids", volume = "22", number = "8", year = "1996", pages = "755-770" } @article{elg1990, author = "H. C. Elman and G. H. Golub", title = "Iterative methods for cyclically reduced non self-adjoint linear systems", journal = MATCOMP, volume = "54", number = "190", year = "1990", pages = "671-700" } @article{elg1992, author = "H. C. Elman and G. H. Golub", title = "Line iterative methods for cyclically reduced discrete convection-diffusion problems", journal = SISSC, volume = "13", number = "1", year = "1992", pages = "339-363" } @article{elg1990b, author = "H. C. Elman and G. H. Golub", title = "Iterative methods for cyclically reduced non self-adjoint linear systems {II}", journal = MATCOMP, volume = "56", year = "1990", pages = "215-242" } @article{elg1994, author = "H. C. Elman and G. H. Golub", title = "Inexact and preconditioned {U}zawa algorithms for saddle point problems", journal = SINUM, volume = "31", number = "6", year = "1994", pages = "1645-1661" } @article{elgs1994, author = "H. C. Elman and G. H. Golub and G. Starke", title = "On the convergence of line iterative methods for cyclically reduced non-symmetrizable linear systems", journal = NUMAT, volume = "67", number = "2", year = "1994", pages = "177-190" } @article{elgu1993, author = "H. C. Elman and X.-Z. Guo", title = "Performance enhancements and parallel algorithms for two multilevel preconditioners", journal = SISC, volume = "14", number = "4", year = "1993", pages = "890-913" } @article{els1986, author = "H. C. Elman and M. H. Schultz", title = "Preconditioning by fast direct methods for non self adjoint nonseparable elliptic equations", journal = SINUM, volume = "23", number = "1", year = "1986", pages = "44-57" } @article{elsi1996, author = "H. C. Elman and D. Silvester", title = "Fast nonsymmetric iterations and preconditioning for {Navier-Stokes} equations", journal = SISC, volume = "17", number = "1", year = "1996", pages = "33-46" } @article{eln1984, author = "L. Elsner", title = "A note on optimal block-scaling of matrices", journal = NUMAT, volume = "44", year = "1984", pages = "127-128" } @article{erh1990, author = "J. Erhel", title = "Sparse matrix multiplication on vector computers", journal = IJHSC, volume = "2", number = "2", year = "1990", pages = "101-116" } @article{erh1995, author = "J. Erhel", title = "A parallel {GMRES} version for general sparse matrices", journal = ETNA, volume = "3", number = "12", year = "1995", pages = "160-176" } @article{eg2000, author = "J. Erhel and F. Guyomarc'h", title = "An augmented conjugate gradient algorithm for solving consecutive symmetric positive definite linear systems", journal = SIMAX, volume = "21", number = "4", year = "2000", pages = "1279-1299" } @article{ebp1996, author = "J. Erhel and K. Burrage and B. Pohl", title = "Restarted {GMRES} preconditioned by deflation", journal = JCAM, volume = "69", number = "2", year = "1996", pages = "303-318" } @article{eglps1987, author = "A. M. Erisman and R. G. Grimes and J. G. Lewis and W. G. {Poole Jr} and H. D. Simon", title = "Evaluation of orderings for unsymmetric sparse matrices", journal = SISSC, volume = "8", number = "4", year = "1987", pages = "600-624" } @article{ev1967, author = "D. J. Evans", title = "The use of preconditioning in iterative method for solving linear equations with symmetric positive definite matrices", journal = JIMA, volume = "4", year = "1967", pages = "295-314" } @book{ev1985, author = "D. J. Evans", title = "Sparsity and its Applications", publisher = "Cambridge University Press", year = "1985" } @article{fm1984, author = "V. Faber and T. Manteuffel", title = "Necessary and sufficient conditions for the existence of a conjugate gradient method", journal = SINUM, volume = "21", number = "2", year = "1984", pages = "352-362" } @article{fm1987, author = "V. Faber and T. Manteuffel", title = "Orthogonal error methods", journal = SINUM, volume = "24", year = "1987", pages = "170-187" } @article{fjkm1996, author = "V. Faber and W. Joubert and E. Knill and T. Manteuffel", title = "Minimal residual method stronger than polynomial preconditioning", journal = SIMAX, volume = "17", number = "4", year = "1996", pages = "707-729" } @article{fad1981, author = "D. K. Faddeev", title = "Properties of the inverse of a {H}essenberg matrix", note = "in Numerical Methods and Computational Issues, volume 5, V. P. Il'in and V. N. Kublanoskaya Eds., 1981 (in Russian)", journal = JSM, volume = "24", number = "1", year = "1984", pages = "118-120" } @book{ff1960, author = "D. K. Faddeev and V. N. Faddeeva", title = "Computational Methods of Linear Algebra", publisher = "Freeman \& Co", address = "San Francisco and London", year = "1963", note = "Original Moscow (1960)" } @article{far1988, author = "C. Farhat", title = "A simple and efficient automatic {FEM} domain decomposer", journal = "Computer and Structures", volume = "28", number = "5", year = "1988", pages = "579-602" } @article{fls1995, author = "C. Farhat and S. Lanteri and H. D. Simon", title = "{TOP/DOMDEC} a software tool for mesh partitioning and parallel processing", journal ="Comput. Syst. Eng.", volume = "6", year = "1995", pages = "13-26" } @article{fed1961, author = "R. P. Fedorenko", title = "A relaxation method for solving elliptic difference equations", journal = ZVM, volume = "1", year = "1961", pages = "922-927", note = "Also in {\it U.S.S.R. Comput. Math. and Math. Phys.}, 1 (1962), pp. 1092-1096" } @article{fer1986, author = "W. E. {Ferguson Jr.}", title = "The rate of convergence of a class of block {J}acobi schemes", journal = SINUM, volume = "23", number = "2", year = "1986", pages = "297-303" } @misc{fim1982, author = "C. M. Fiduccia and R. M. Mattheyses", title = "A linear-time heuristic for improving network partitions", howpublished = "19th Design Automation Conference, IEEE", year = "1982" } @article{fie1975, author = "M. Fiedler", title = "A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory", journal = "Czechoslovak Math. J.", volume = "25", year = "1975", pages = "619-633" } @book{fie1986, author = "M. Fiedler", title = "Special Matrices and their Applications in Numerical Mathematics", edition = "1st", publisher = "Martinus Nijhoff Publishers", address = "Dordrecht, The Netherlands", year = "1986", note = "reprinted by Dover (2008)" } @article{fip1962, author = "M. Fiedler and V. Pt{\'{a}}k", title = "On matrices with non-positive off-diagonal elements and positive principal minors", journal = CZMJ, volume = "12", number = "3", year = "1962", pages = "382-400" } @article{fk1988, author = "S. A. Finogenov and Y. A. Kuznetsov", title = "Two-stage fictitious components method for solving the {D}irichlet boundary value problem", journal = "Sov. J. Numer. Anal. Math. Modelling", volume = "3", number = "4", year = "1988", pages = "301-323" } @book{fis1996, author = "B. Fischer", title = "Polynomial Based Iteration Methods for Symmetric Linear Systems", publisher = "Wiley Teubner", year = "1996" } @inproceedings{fisf1994, author = "B. Fischer and R. W. Freund", title = "An inner product-free conjugate gradient-like for {H}ermitian positive definite systems", booktitle = "Proceedings of the Cornelius Lanczos International Centenary Conference", editor = "J. Brown and M. Chu and D. Ellison and R. J. Plemmons", publisher = "SIAM", year = "1994", pages = "288-290" } @article{fig1991, author = "B. Fischer and G. H. Golub", title = "On generating polynomials which are orthogonal over several intervals", journal = MATCOMP, volume = "56", number = "194", year = "1991", pages = "711-730" } @inproceedings{fig1993, author = "B. Fischer and G. H. Golub", title = "On the error computation for polynomial based iteration methods", booktitle = "Recent Advances in Iterative Methods", editor = "A. Greenbaum and M. Luskin", publisher = "Springer", address = "New York", year = "1994", pages = "59-67" } @article{fr1989, author = "B. Fischer and L. Reichel", title = "A stable {R}ichardson iteration method for complex linear systems", journal = NUMAT, volume = "54", number = "2", year = "1989", pages = "225-242" } @article{fiu1969, author = "C. F. Fischer and R. A. Usmani", title = "Properties of some tridiagonal matrices and their application to boundary value problems", journal = SINUM, volume = "6", number = "1", year = "1969", pages = "127-142" } @article{fghlw1974, author = "D. Fischer and G. H. Golub and O. Hald and C. Leiva and O. B. Widlund", title = "Fourier-{T}oeplitz methods for separable elliptic equations", journal = MATCOMP, volume = "28", number = "126", year = "1974", pages = "349-368" } @article{fil1971, author = "G. J. Fix and K. Larsen", title = "On the convergence of {SOR} iterations for finite element approximations to elliptic boundary value problems", journal = SINUM, volume = "", number = "", year = "1971", pages = "536-547" } @inproceedings{fl1976, author = "R. Fletcher", title = "Conjugate gradient methods for indefinite systems", booktitle = "Numerical Analysis. Lecture Notes in Mathematics, vol 506", editor = "G. A. Watson", publisher = "Springer", address = "Berlin, Heidelberg", year = "1976", pages = "73-89" } @article{fl1976b, author = "R. Fletcher", title = "Factorizing symmetric indefinite matrices", journal = LAA, volume = "14", year = "1976", pages = "257-272" } @article{fsvdv1996, author = "D. R. Fokkema and G. L. G. Sleijpen and H. van der Vorst", title = "Generalized conjugate gradient squared", journal = JCAM, volume = "71", number = "1", year = "1996", pages = "125-146" } @inproceedings{foj1977, author = "K. W. Fong and T. L. Jordan", title = "Some linear algebraic algorithms and their performance on {CRAY-1}", booktitle = "High-Speed Computer and Algorithm Organization", editor = "D. J. Kuck and D. H. Lawrie and A. H. Sameh", publisher = "Academic Press", year = "1977", pages = "313-316" } @article{for1981, author = "B. Fornberg", title = "A vector implementation of the fast {F}ourier transform algorithm", journal = MATCOMP, volume = "36", number = "153", year = "1981", pages = "189-191" } @article{for1953, author = "G. E. Forsythe", title = "Solving linear algebraic equations can be interesting", journal = BAMS, volume = "59", number = "4", year = "1953", pages = "299-329" } @article{for1953c, author = "G. E. Forsythe", title = "Tentative classification of methods and bibliography on solving systems of linear equations", journal = JNBS, volume = "29", year = "1953", pages = "1-28" } @book{fmm1977, author = "G. E. Forsythe and M. A. Malcolm and C. B. Moler", title = "Computer Methods for Mathematical Computations", publisher = "Prentice-Hall, Inc.", address = "Englewood Cliffs, N. J.", year = "1977" } @book{fm1967, author = "G. E. Forsythe and C. B. Moler", title = "Computer Solution of Linear Algebraic Systems", publisher = "Prentice-Hall, Inc.", address = "Englewood Cliffs, N. J.", year = "1967" } @article{fos1955, author = "G. E. Forsythe and E. G. Straus", title = "On best conditioned matrices", journal = PAMS, volume = "6", year = "1955", pages = "340-345" } @book{fw1960, author = "G. E. Forsythe and W. R. Wasow", title = "Finite-difference Methods for Partial Differential Equations", publisher = "John Wyley and Sons", year = "1960" } @article{fos1994, author = "L. V. Foster", title = "Gaussian elimination with partial pivoting can fail in practice", journal = SIMAX, volume = "15", number = "4", year = "1994", pages = "1354-1362" } @book{fo1964, author = "L. Fox", title = "An Introduction to Numerical Linear Algebra", publisher = "Oxford University Press", year = "1964" } @article{fo1948, author = " L. Fox and H. D. Huskey and J. H. Wilkinson", title = "Notes on the solution of linear algebraic equations", journal = QJMAM, volume = "1", year = "1948", pages = "149-173" } @techreport{fra1995, author = "J. Francescatto", title = "R{\'e}solution de l'{\'e}quation de {P}oisson sur des maillages {\'e}tir{\'e}s par une m{\'e}thode multigrille", institution = "INRIA", number = "2712", year = "1995" } @techreport{frad1997, author = "J. Francescatto and A. Dervieux", title = "A semi coarsening strategy for unstructured {MG} with agglomeration", institution = "INRIA", number = "2950", year = "1997" } @inproceedings{fmb1988, author = "P. O. Frederickson and O. A. McBryan", title = "Parallel superconvergent multigrid", booktitle = "Multigrid Methods", editor = "S. F. McCormick", publisher = "Marcel Dekker", year = "1988", pages = "195-210" } @article{fr1990, author = "R. W. Freund", title = "On conjugate gradient type methods and polynomial preconditioners for a class of complex non {H}ermitian matrices", journal = NUMAT, volume = "57", year = "1990", pages = "285-312" } @techreport{fr1991, author = "R. W. Freund", title = "Krylov subspace methods for complex non {H}ermitian linear systems", institution = "RIACS NASA Ames", number = "91.11", year = "1991" } @article{fr1992, author = "R. W. Freund", title = "Quasi-kernel polynomials and their use in non-{H}ermitian matrix iterations", journal = JCAM, volume = "43", number = "1-2", year = "1992", pages = "135-158" } @article{fr1992b, author = "R. W. Freund", title = "Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices", journal = SISSC, volume = "13", year = "1992", pages = "425-448" } @article{fr1993, author = "R. W. Freund", title = "A transpose-free quasi-minimal residual algorithm for non-{H}ermitian linear systems", journal = SISC, volume = "14", number = "2", year = "1993", pages = "470-482" } @article{fn1991, author = "R. W. Freund and N. M. Nachtigal", title = "{QMR}: a quasi-minimal residual method for non-{H}ermitian linear systems", journal = NUMAT, volume = "60", number = "3", year = "1991", pages = "315-339" } @article{fgn1992, author = "R. W. Freund and G. H. Golub and N. M. Nachtigal", title = "Iterative solution of linear systems", journal = ACTNUM, volume = "1", year = "1992", pages = "57-100" } @article{fgn1993, author = "R. W. Freund and M. H. Gutknecht and N. M. Nachtigal", title = "An implementation of the look-ahead {L}anczos algorithm for non-{H}ermitian matrices", journal = SISC, volume = "14", year = "1993", pages = "137-158" } @inproceedings{fh1991, author = "R. W. Freund and M. Hochbruck", title = "A biconjugate gradient type algorithm on massively parallel architectures", booktitle = "IMACS'91", editor = "R. Vichnevetsky and J. J. H. Miller", publisher = "Criterion Press", address = "Dublin", year = "1991", pages = "720-721" } @article{fm1997, author = "R. W. Freund and M. Malhotra", title = "A block {QMR} algorithm for non-{H}ermitian linear systems with multiple right-hand sides", journal = LAA, volume = "254", number = "1-3", year = "1997", pages = "119-157" } @techreport{fs1991, author = "R. W. Freund and T. Szeto", title = "A quasi-minimal residual squared algorithm for non-{H}ermitian linear systems", number = "91.26", institution = "RIACS, NASA Ames Research Center", year = "1991" } @inProceedings{frj1998, author = "M. Frigo and S. G. Johnson", title = "{FFTW}: {A}n adaptive software architecture for the {FFT}", booktitle = "Proc. 1998 IEEE Intl. Conf. Acoustics Speech and Signal Processing", publisher = "IEEE", year = "1998", pages = "1381-1384" } @article{frj2005, author = "M. Frigo and S. G. Johnson", title = "The Design and Implementation of {FFTW3}", journal = "Proceedings of the IEEE", volume = "93", number = "2", year = "2005", pages = "216-231", note = "Special issue on ``Program Generation, Optimization, and Platform Adaptation''" } @inproceedings{fd1991, author = "S. Fujino and S. Doi", title = "Optimizing multicolor {ICCG} methods on some vector computers", booktitle = "Proceedings IMACS Int. Symp. Iterative Methods in Linear Algebra", editor = "R. Beauwens", publisher = "North Holland", year = "1991" } @article{fnp1982, author = "R. E. Funderlic and M. Neumann and R. J. Plemmons", title = "{LU} decompositions of generalized diagonally dominant matrices", journal = NUMAT, volume = "40", year = "1982", pages = "57-69" } @article{fp1981, author = "R. E. Funderlic and R. J. Plemmons", title = "{LU} decomposition of {M}-matrices by elimination without pivoting", journal = LAA, volume = "41", year = "1981", pages = "41-99" } @book{ghno1990, author = "K. A. Gallivan and M. T. Heath and E. G. Ng and J. M. Ortega and B. W. Peyton and R. J. Plemmons and C. H. Romine and A. H. Sameh and R. C. Voigt", title = "Parallel Algorithms for Matrix Computations", publisher = "SIAM", year = "1990" } @article{gpsa1990, author = "K. A. Gallivan and R. J. Plemmons and A. H. Sameh", title = "Parallel algorithms for dense linear algebra computations", journal = SIREV, volume = "32", number = "1", year = "1990", pages = "54-135" } @article{gas1989, author = " E. Gallopoulos and Y. Saad", title = "A parallel block cyclic reduction algorithm for the fast solution of elliptic equations", journal = PARCOMP, volume = "10", year = "1989", pages = "143-159" } @inproceedings{ggg1990, author = "W. Gander and G. H. Golub and D. Gruntz", title = "Solving linear equations by extrapolation", booktitle = "Supercomputing (NATO ASI Series)", editor = "J. S. Kowalik", publisher = "Springer", year = "1990", pages = "279-293" } @article{gvr1986, author = "D. Gannon and J. {Van Rosendale}", title = "On the structure of parallelism in a highly concurrent {PDE} solver", journal = "J. Par. Dist. Comp.", volume = "3", year = "1986", pages = "106-135" } @book{ga1959, author = "F. R. Gantmacher", title = "The Theory of Matrices, {V}ol. 1", publisher = "AMS Chelsea Publishing", address = "Providence, RI", year = "1959" } @article{gar1996, author = "M. Garbey", title = "A {S}chwarz alternating procedure for singular perturbation problems", journal = SISC, volume = "17", number = "5", year = "1996", pages = "1175-1201" } @article{gms1983, author = "J. Gary and S. F. McCormick and R. A. Sweet", title = "Successive overrelaxation, multigrid, and preconditioned conjugate gradients algorithms for solving a diffusion problem on a vector computer", journal = AMC, volume = "13", year = "1983", pages = "285-310" } @article{gau1968, author = "W. Gautschi", title = "Construction of {Gauss–Christoffel} quadrature formulas", journal = MATCOMP, volume = "23", year = "1968", pages = "221-230" } @article{gau1985, author = "W. Gautschi", title = "Orthogonal polynomials - constructive theory and applications", journal = JCAM, volume = "12-13", year = "1985", pages = "61-76" } @techreport{gei1985, author = "G. A. Geist", title = "Efficient parallel {LU} factorization with pivoting on a hypercube multiprocessor", institution = "Oak Ridge Nat. Laboratory", number = "ORNL–6211", year = "1985" } @article{gei1989, author = "G. A. Geist", title = "Task scheduling for parallel sparse {C}holesky factorization", journal = "Int. J. Parallel Prog.", volume = "18", number = "4", year = "1989", pages = "291-314" } @article{ger1988, author = "G. A. Geist and C. H. Romine", title = "{LU} factorization algorithms on distributed memory multiprocessor architectures", journal = SISSC, volume = "9", number = "4", year = "1988", pages = "639-649" } @article{gen1987, author = "W. Gentzsch", title = "A fully vectorizable {SOR} variant", journal = PARCOMP, volume = "4", year = "1987", pages = "349-353" } @article{geo1973, author = "J. A. George", title = "Nested dissection of a regular finite element mesh", journal = SINUM, volume = "10", number = "2", year = "1973", pages = "345-363" } @article{geo1974, author = "J. A. George", title = "On block elimination for sparse linear systems", journal = SINUM, volume = "11", number = "3", year = "1974", pages = "585-603" } @article{geo1977, author = "J. A. George", title = "Numerical experiments using dissection methods to solve $n$ by $n$ grid problems", journal = SINUM, volume = "14", number = "2", year = "1977", pages = "161-179" } @article{geo1980, author = "J. A. George", title = "An automatic one way dissection algorithm for irregular finite element problems", journal = SINUM, volume = "17", number = "6", year = "1980", pages = "740-751" } @book{ggl1993, author = "J. A. George and J. R. Gilbert and J. W. H. Liu Eds.", title = "Graph Theory and Sparse Matrix Computation", publisher = "Springer Verlag", year = "1993" } @article{ghl19896, author = "J. A. George and M. T. Heath and J. W. H. Liu", title = "Parallel {C}holesky factorization on a shared memory multiprocessor", journal = LAA, volume = "77", year = "1986", pages = "165-187" } @article{ghln19898, author = "J. A. George and M. T. Heath and J. W. H. Liu and E. G. Ng", title = "Sparse {C}holesky factorization on a local memory multiprocessor", journal = SISSC, volume = "9", number = "2", year = "1988", pages = "327–340" } @article{geol1975, author = "J. A. George and J. W. H. Liu", title = "A note on fill for sparse matrices", journal = SINUM, volume = "12", number = "3", year = "1975", pages = "452–455" } @article{gel1978b, author = "J. A. George and J. W. H. Liu", title = "Algorithms for matrix partitioning and the numerical solution of finite element systems", journal = SINUM, volume = "15", number = "2", year = "1978", pages = "297-327" } @article{gl1978, author = "J. A. George and J. W. H. Liu", title = "An automatic nested dissection algorithm for irregular finite element problems", journal = SINUM, volume = "15", number = "5", year = "1978", pages = "1053-1069" } @article{gl1979, author = "J. A. George and J. W. H. Liu", title = "An implementation of a pseudo-peripheral node finder", journal = TOMS, volume = "5", number = "3", year = "1979", pages = "284-295" } @article{gl1979b, author = "J. A. George and J. W. H. Liu", title = "The design of a user interface for a sparse matrix package", journal = TOMS, volume = "5", number = "2", year = "1979", pages = "139-162" } @article{gl1980, author = "J. A. George and J. W. H. Liu", title = "A minimal storage implementation of the minimum degree algorithm", journal = SINUM, volume = "17", number = "2", year = "1980", pages = "282-299" } @article{gl1980b, author = "J. A. George and J. W. H. Liu", title = "An optimal algorithm for symbolic factorization of symmetric matrices", journal = SIC, volume = "9", number = "3", year = "1980", pages = "583-593" } @article{gl1980c, author = "J. A. George and J. W. H. Liu", title = "A fast implementation of the minimum degree algorithm using quotient graphs", journal = TOMS, volume = "6", number = "3", year = "1980", pages = "337-358" } @book{gl1981, author = "J. A. George and J. W. H. Liu", title = "Computer Solution of Large Sparse Positive Definite Systems", publisher = "Prentice Hall", year = "1981" } @article{gl1989, author = "J. A. George and J. W. H. Liu", title = "The evolution of the minimum degree ordering algorithm", journal = SIREV, volume = "31", number = "1", year = "1989", pages = "1-19" } @article{gln1988, author = "J. A. George and J. W. H. Liu and E. G. Ng", title = "A data structure for sparse {QR} and {LU} factorizations", journal = SISSC, volume = "9", number = "1", year = "1988", pages = "100-121" } @article{gln1989, author = "J. A. George and J. W. H. Liu and E. G. Ng", title = "Communication results for parallel sparse {C}holesky factorization on a hypercube", journal = PARCOMP, volume = "10", number = "3", year = "1989", pages = "287-298" } @article{geom1978, author = "J. A. George and D. R. McIntyre", title = "On the application of the minimum degree algorithm to finite element systems", journal = SINUM, volume = "15", number = "1", year = "1978", pages = "90-112" } @article{geon1985, author = "J. A. George and E. G. Ng", title = "An implementation of {G}aussian elimination with partial pivoting for sparse systems", journal = SISSC, volume = "6", number = "2", year = "1985", pages = "390-409" } @article{geon1987, author = "J. A. George and E. G. Ng", title = "Symbolic factorization for sparse {G}aussian elimination with partial pivoting", journal = SISSC, volume = "8", number = "6", year = "1987", pages = "877-898" } @article{geon1988, author = "J. A. George and E. G. Ng", title = "On the complexity of sparse {QR} and {LU} factorization for finite element matrices", journal = SISSC, volume = "9", number = "5", year = "1988", pages = "849-861" } @article{gpv1978, author = "J. A. George and W. G. Poole and R. G. Voigt", title = "Incomplete nested dissection for solving $n$ by $n$ grid problems", journal = SINUM, volume = "15", number = "4", year = "1978", pages = "662-673" } @article{gpo1997, author = "J. A. George and A. Pothen", title = "An analysis of spectral envelope reduction via quadratic assignment problems", journal = SIMAX, volume = "18", number = "3", year = "1997", pages = "706-732" } @article{geor1980, author = "J. A. George and H. Rashwan", title = "On symbolic factorization of partitioned sparse symmetric matrices", journal = LAA, volume = "34", year = "1980", pages = "145-157" } @article{gps1976, author = "N. E. Gibbs and W. G. {Poole Jr.} and P. K. Stockmeyer", title = "An algorithm for reducing the bandwidth and profile of a sparse matrix", journal = SINUM, volume = "13", number = "2", year = "1976", pages = "236-250" } @article{gps1976b, author = "N. E. Gibbs and W. G. {Poole Jr.} and P. K. Stockmeyer", title = "A comparison of several bandwidth and profile reduction algorithms", journal = TOMS, volume = "2", year = "1976", pages = "322-330" } @article{ggk1998, author = "E. Giladi and G. H. Golub and J. B. Keller", title = "Inner and outer iterations for the {C}hebyshev algorithm", journal = SINUM, volume = "35", number = "1", year = "1998", pages = "300-319" } @article{gil1994, author = "J. R. Gilbert", title = "Predicting structure in sparse matrix computations", journal = SIMAX, volume = "15", number = "1", year = "1994", pages = "62-79" } @article{gih1990, author = "J. R. Gilbert and H. Hafsteinsson", title = "Parallel symbolic factorization of sparse linear systems", journal = PARCOMP, volume = "14", year = "1990", pages = "151-162" } @article{gli1993, author = "J. R. Gilbert and J. W. H. Liu", title = "Elimination structures for unsymmetric sparse {LU} factors", journal = SIMAX, volume = "14", number = "2", year = "1993", pages = "334-352" } @article{ggm1998, author = "J. R. Gilbert and G. L. Miller and S.-H. Teng", title = "Geometric mesh partitioning: {I}mplementation and experiments", journal = SISC, volume = "19", number = "6", year = "1998", pages = "2091-2110" } @article{gnp1994, author = "J. R. Gilbert and E. G. Ng and B. W. Peyton", title = "An efficient algorithm to compute row and column counts for sparse {C}holesky factorization", journal = SIMAX, volume = "15", number = "4", year = "1994", pages = "1075-1091" } @article{gp1988, author = "J. R. Gilbert and T. Peierls", title = "Sparse partial pivoting in time proportional to arithmetic operations", journal = SISSC, volume = "9", number = "5", year = "1988", pages = "862-874" } @article{gis1992, author = "J. R. Gilbert and R. S. Schreiber", title = "Highly parallel sparse {C}holesky factorization", journal = SISSC, volume = "13", number = "5", year = "1992", pages = "1151-1172" } @article{giz1990, author = "J. R. Gilbert and E. Zmijewski", title = "A parallel graph partitioning algorithm for a message passing multiprocessor", journal = "Int. J. Parallel Prog.", volume = "16", year = "1990", pages = "427-449" } @article{ggms1974, author = "P. E. Gill and G. H. Golub and W. Murray and M. A. Saunders", title = "Methods for modifying matrix factorizations", journal = MATCOMP, volume = "28", number = "126", year = "1974", pages = "505-535" } @article{gms1975, author = "P. E. Gill and W. Murray and M. A. Saunders", title = "Methods for computing and modifying the {LDV} factors of a matrix", journal = MATCOMP, volume = "29", number = "132", year = "1975", pages = "1051-1077" } @book{ggmp1988, author = "R. Glowinski and G. H. Golub and G. Meurant and J. Périaux Eds.", title = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", publisher = "SIAM", year = "1988" } @book{gkmpb1991, author = "R. Glowinski and Y. A. Kuznetsov and G. Meurant and J. Périaux and O. B. Widlund Eds.", title = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", publisher = "SIAM", year = "1991" } @inproceedings{gpt1990, author = "R. Glowinski and J. Périaux and G. Terrasson", title = "On the coupling of viscous and inviscid models for compressible fluid flows via domain decomposition", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1990", pages = "64-97" } @article{gbg1991, author = "D. Golberg", title = "What every computer scientist should know about floating point arithmetic", journal = "ACM Comp. Surveys", volume = "23", number = "1", year = "1991", pages = "5-48" } @article{gdb1972, author = "D. Goldfarb", title = "Modification methods for inverting matrices and solving systems of linear algebraic equations", journal = MATCOMP, volume = "26", number = "120", year = "1972", pages = "829-852" } @book{gol1977, author = "H. H. Goldstine", title = "A History of Numerical Analysis from the 16th through the 19th Century", publisher = "Springer", year = "1977" } @article{go1962, author = "G. H. Golub", title = "Bounds for the round-off errors in the {R}ichardson second order method", journal = BITNM, volume = "2", number = "4", year = "1962", pages = "212-223" } @article{go1973, author = "G. H. Golub", title = "Some modified matrix eigenvalue problems", journal = SIREV, volume = "15", number = "2", year = "1973", pages = "318-334" } @article{go1974, author = "G. H. Golub", title = "Bounds for matrix moments", journal = RMJM, volume = "4", number = "2", year = "1974", pages = "207-211" } @book{go1984, author = "G. H. {Golub Ed.}", title = "Studies in Numerical Analysis", publisher = "The Mathematical Association of America", year = "1984" } @inproceedings{godp1990, author = "G. H. Golub and J. E. {de Pillis}", title = "Toward an effective two-parameter {SOR} method", booktitle = "Iterative Methods for Large Linear Systems", editor = " D. R. Kincaid and L. J. Hayes", publisher = "Academic Press", year = "1990", pages = "107-119" } @article{gog1990, author = "G. H. Golub and M. H. Gutknecht", title = "Modified moments for indefinite weight functions", journal = NUMAT, volume = "57", year = "1990", pages = "607-624" } @article{gok1986, author = "G. H. Golub and R. Kannan", title = "Convergence of a two-stage {R}ichardson process for non linear equations", journal = BITNM, volume = "26", number = "2", year = "1986", pages = "209-216" } @article{gok1983, author = "G. H. Golub and J. Kautsky", title = "Calculation of {G}auss quadratures with multiple free and fixed knots", journal = NUMAT, volume = "41", year = "1983", pages = "147-163" } @inproceedings{gma1984, author = "G. H. Golub and D. Mayers", title = "The use of preconditioning over irregular regions", booktitle = "Computing Methods in Applied Science and Engineering VI", editor = "R. Glowinski and J. L. Lions", publisher = "North-Holland", year = "1984", pages = "3-14" } @book{gom1983, author = "G. H. Golub and G. Meurant", title = "Résolution Numérique des Grands Systèmes Linéaires", publisher = "Eyrolles", year = "1983" } @inproceedings{gm1994, author = "G. H. Golub and G. Meurant", title = "Matrices, moments and quadrature", booktitle = "Numerical Analysis 1993", editor = "D. F. Griffiths and G. A. Watson", series = "Pitman Research Notes in Mathematics", volume = "303", publisher = "Longman Sci. Tech.", year = "1994", pages = "105-156", note = "Reprinted in \cite{cgl2007}" } @article{gme1997, author = "G. H. Golub and G. Meurant", title = "Matrices, moments and quadrature {II} or how to compute the norm of the error in iterative methods", journal = BIT, volume = "37", number = "3", year = "1997", pages = "687-705" } @article{gol1989, author = "G. H. Golub and D. P. {O{'}Leary}", title = "Some history of the conjugate gradient and {L}anczos algorithms: 1948-1976", journal = SIREV, volume = "31", number = "1", year = "1989", pages = "50-102" } @book{goo1992, author = "G. H. Golub and J. M. Ortega", title = "Scientific Computing and Differential Equations, an Introduction to Numerical Methods", publisher = "Academic Press", year = "1992" } @techreport{gov1981, author = "G. H. Golub and M. L. Overton", title = "Convergence of a two-stage {R}ichardson iterative procedure for solving systems of linear equations", institution = "Computer Science Dept., Stanford University", number = "NA-81-17", year ="1981" } @article{gov1988, author = "G. H. Golub and M. L. Overton", title = "The convergence of inexact {C}hebyshev and {R}ichardson iterative methods for solving linear systems", journal = NUMAT, volume = "53", number = "5", year = "1988", pages = "571-593" } @article{gs1994, author = "G. H. Golub and Z. Strako{\v{s}}", title = "Estimates in quadratic formulas", journal = NUMALGO, volume = "8", number = "2", year = "1994", pages = "241-268" } @inproceedings{gu1977, author = "G. H. Golub and R. Underwood", title = "The block {L}anczos method for computing eigenvalues", booktitle = "Mathematical Software {III}, Proceedings of a Symposium conducted by the Mathematics Research Center, the University of Wisconsin-Madison, March 28{-}30, 1977", editor = "J. Rice", publisher = "Academic Press", year = "1977", pages = "361-377" } @incollection{gvdv1997, author = "G. H. Golub and H. A. {van der Vorst}", title = "Closer to the solutions: {I}terative linear solvers", booktitle = "The State of the Art in Numerical Analysis", editor = "I. S. Duff and G. A. Watson", publisher = "Oxford University Press", year = "1997", pages = "63-92" } @article{gv1979, author = "G. H. Golub and C. F. {Van Loan}", title = "Unsymmetric positive definite linear systems", journal = LAA, volume = "28", year = "1979", pages = "85-97" } @book{gvl1989, author = "G. H. Golub and C. F. {Van Loan}", title = "Matrix {C}omputations", edition = "2nd", publisher = "Johns Hopkins University Press", address = "Baltimore", year = "1989" } @book{gvl1996, author = "G. H. Golub and C. F. {Van Loan}", title = "Matrix {C}omputations", edition = "3rd", publisher = "Johns Hopkins University Press", address = "Baltimore", year = "1996" } @article{gov1974, author = "G. H. Golub and J. M. Varah", title = "On a characterization of the best $\ell_2$-scaling of a matrix", journal = SINUM, volume = "11", number = "3", year = "1974", pages = "472-479" } @article{go1961, author = "G. H. Golub and R. S. Varga", title = "{Chebyshev} semi-iterative methods, successive overrelaxation iterative Methods, and second order {Richardson} iterative methods. {I}", journal = NUMAT, volume = "3", number = "1", year = "1961", pages = "147-156" } @article{go1961b, author = "G. H. Golub and R. S. Varga", title = "{Chebyshev} semi-iterative methods, successive overrelaxation iterative Methods, and second order {Richardson} iterative methods. {II}", journal = NUMAT, volume = "3", number = "1", year = "1961", pages = "157-168" } @article{gw1969, author = "G. H. Golub and J. H. Welsch", title = "Calculation of {Gauss} quadrature rules", journal = MATCOMP, volume = "23", number = "106", year = "1969", pages = "221-230" } @article{gy1999, author = "G. H. Golub and Q. Ye", title = "Inexact preconditioned conjugate gradient method with inner-outer iteration", journal = SISC, volume = "21", number = "4", year = "1999", pages = "1305-1320" } @phdthesis{goz1986, author = "R. Gonzalez", title = "Domain decomposition for two dimensional elliptic operators on vector and parallel machines", school = "Rice University", year = "1986" } @article{goo1958, author = "I. J. Good", title = "The interaction algorithm and practical {F}ourier analysis", journal = "J. Roy. Statist. Soc. Ser. B", volume = "20", year = "1958", pages = "361-372" } @article{goo1971, author = "I. J. Good", title = "The relationship between two {Fast Fourier Transforms}", journal = "IEEE Trans. Comput.", volume = "20", year = "1971", pages = "310-317" } @phdthesis{gvs1990, author = "D. Goovaerts", title = "Domain decomposition for elliptic partial differential equations", school = "Katholieke Universiteit Leuven", year = "1990" } @article{gou1991, author = "N. Gould", title = "On growth in {G}aussian elimination with complete pivoting", journal =SIMAX, volume = "12", number = "2", year = "1991", pages = "354-361" } @article{gos1998, author = "N. I. Gould and J. A. Scott", title = "Sparse approximate-inverse preconditioners using norm-minimization techniques", journal = SISC, volume = "19", number = "2", year = "1998", pages = "605-625" } @article{goou1968, author = "A. R. Gourlay", title = "The acceleration of the {Peaceman-Rachford} method by {C}hebyshev polynomials", journal = COMPJ, volume = "10", year = "1968", pages = "378-382" } @article{goou1970, author = "A. R. Gourlay", title = "On {C}hebychev acceleration procedures for alternating direction iterative methods", journal = JIMA, volume = "6", year = "1970", pages = "1-11" } @article{grar1987, author = "W. B. Gragg and L. Reichel", title = "On the application of orthogonal polynomials to the iterative solution of linear systems of equations with indefinite or non-{H}ermitian matrices", journal = LAA, volume = "88", year = "1987", pages = "349-371" } @article{ggr1997, author = "T. Grauschopf and M. Griebel and H. Regler", title = "Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic {PDE}s", journal = ANM, volume = "23", number = "1", year = "1997", pages = "63-95" } @phdthesis{grc1981, author = "J. F. Grcar", title = "Analysis of the {L}anczos algorithm and of the approximation problem in {R}ichardson's method", school = "University of Illinois at Urbana-Champaign", address = "USA", year = "1981" } @techreport{grc1989, author = "J. F. Grcar", title = "Operator coefficient methods for linear equations", institution = "Sandia National Laboratory", number = "SAND89-8691", year = "1989" } @techreport{grc1990, author = "J. F. Grcar", title = "Matrix stretching for linear equations", institution = "Sandia National Laboratory", number = "SAND90-8723", year = "1990" } @article{gr1979, author = "A. Greenbaum", title = "Comparison of splittings used with the conjugate gradient algorithm", journal = NUMAT, volume = "33", year = "1979", pages = "181-194" } @phdthesis{gr1981, author = "A. Greenbaum", title = "Convergence properties of the conjugate gradient algorithm in exact and finite precision arithmetic", school = "University of California, Berkeley", address = "USA", year = "1981" } @techreport{gr1981b, author = "A. Greenbaum", title = "Behavior of the conjugate gradient algorithm in finite precision arithmetic", institution = "Lawrence Livermore Laboratory", number = "UCRL-85752", year = "1981" } @article{gr1984, author = "A. Greenbaum", title = "Analysis of a multigrid method as an iterative technique for solving linear systems", journal = SINUM, volume = "21", number = "3", year = "1984", pages = "473-485" } @article{gr1989, author = "A. Greenbaum", title = "Behavior of slightly perturbed {L}anczos and conjugate gradient recurrences", journal = LAA, volume = "113", year = "1989", pages = "7-63" } @article{gr1997b, author = "A. Greenbaum", title = "Estimating the attainable accuracy of recursively computed residual methods", journal = SIMAX, volume = "1", number = "3", year = "1997", pages = "535-551" } @book{gr1997, author = "A. Greenbaum", title = "Iterative Methods for Solving Linear Systems", publisher = "SIAM", year = "1997" } @article{grlc1989, author = "A. Greenbaum and C. Li and H. Z. Chao", title = "Parallelizing preconditioned conjugate gradient algorithms", journal = CPC, volume = "53", year = "1989", pages = "295-309" } @article{grr1989, author = "A. Greenbaum and G. H. Rodrigue", title = "Optimal preconditioners of a given sparsity pattern", journal = BITNM, volume = "29", number = "4", year = "1989", pages = "610-634" } @article{grs1992, author = "A. Greenbaum and Z. Strako\v{s}", title = "Predicting the behavior of finite precision {L}anczos and conjugate gradient computations", journal = SIMAX, volume = "13", number = "1", year = "1992", pages = "121-137" } @article{gps1996, author = "A. Greenbaum and V. Pt{\'a}k and Z. Strako\v{s}", title = "Any convergence curve is possible for {GMRES}", journal = SIMAX, volume = "17", number = "3", year = "1996", pages = "465-470" } @article{gt1994, author = "A. Greenbaum and L. N. Trefethen", title = "{GMRES/CR} and {A}rnoldi/{L}anczos as matrix approximation problems", journal = SISC, volume = "15", number = "2", year = "1994", pages = "359-368" } @article{gos1995, author = "M. Griebel and P. Oswald", title = "On the abstract theory of additive and multiplicative {S}chwarz algorithms", journal = NUMAT, volume = "70", year = "1995", pages = "163-180" } @book{grw1989, author = "D. F. Griffiths and G. A. Watson Eds.", title = "Numerical Analysis 1989", publisher = "Longman Scientific and Technical", year = "1989", note = "Vol. 228, Pitman research notes in mathematics series" } @book{grw1994, author = "D. F. Griffiths and G. A. Watson Eds.", title = "Numerical Analysis 1994", publisher = "Longman Scientific and Technical", year = "1994", note = "Vol. 303, Pitman research notes in mathematics series" } @article{grl1981, author = "R. G. Grimes and J. G. Lewis", title = "Condition number estimation for sparse matrices", journal = SISSC, volume = "2", year = "1981", pages = "384-388" } @article{gps1990, author = "R. G. Grimes and D. J. Pierce and H. D. Simon", title = "A new algorithm for finding a pseudoperipheral node in a graph", journal = SIMAX, volume = "11", number = "2", year = "1990", pages = "323-334" } @article{grk1988, author = "W. D. Gropp and D. E. Keyes", title = "Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations", journal = SISSC, volume = "9", year = "1988", pages = "312-326" } @article{grk1992, author = "W. D. Gropp and D. E. Keyes", title = "Domain decomposition with local mesh refinement", journal = SISSC, volume = "13", number = "4", year = "1988", pages = "967–993" } @inproceedings{gs1993, author = "M. J. Grote and H. D. Simon", title = "Parallel preconditioning and approximate inverses on the {C}onnection {M}achine", booktitle = "Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing", editor = "R. Sincovec", publisher = "SIAM", year = "1993", pages = "519-523" } @article{gui1965, author = "W. H. {Guilinger Jr.}", title = "The {Peaceman-Rachford} method for small mesh increments", journal = JMAA, volume = "11", year = "1965", pages = "261-277" } @phdthesis{gul1993, author = "H. Guillard", title = "Convergence analysis of a multilevel relaxation method", school = "INRIA", year = "1993", note = "Rapport 1884, INRIA" } @article{ guo1991, author = "G.-H. Guo", title = "Some results on sparse block factorization iterative methods", journal = LAA, volume = "145", year = "1991", pages = "187-199" } @article{gsk1992, author = "R. Guo and R. D. Skeel", title = "An algebraic hierarchical basis preconditioner", journal = ANM, volume = "9", year = "1992", pages = "21-32" } @article{gks1995, author = "A. Gupta and V. Kumar and A. H. Sameh", title = "Performance and scalability of preconditioned conjugate gradient methods on parallel computers", journal = "EEE Trans. Parallel Distrib. Syst.", volume = "6", number = "5", year = "1995", pages = "455-469" } @article{gum1986, author = "M. M. Gupta", title = "A spectrum envelope technique for iterative solution of central difference approximations of convection-diffusion equations", journal = SIADM, volume = "7", number = "4", year = "1986", pages = "513-526" } @article{gui1978, author = "I. Gustafsson", title = "A class of first order factorization methods", journal = BIT, volume = "18", year = "1978", pages = "142-156" } @article{gui1979, author = "I. Gustafsson", title = "On modified incomplete {C}holesky factorization methods for the solution of problems with mixed boundary conditions and problems with discontinuous material coefficients", journal = IJNME, volume = "14", year = "1979", pages = "1127-1140" } @article{gui1984, author = "I. Gustafsson", title = "A preconditioned iterative method for the solution of the biharmonic problem", journal = IMAJNA, volume = "4", year = "1984", pages = "55–67" } @article{gul1986, author = "I. Gustafsson and G. Lindskog", title = "A preconditioning technique based on element matrix factorization", journal = CMAME, volume = "55", year = "1986", pages = "201-220" } @article{gu1988, author = "M. H. Gutknecht", title = "Stationary and almost stationary iterative $(k,l)$-step methods for linear and nonlinear systems of equations", journal = NUMAT, volume = "56", number = "2", year = "1988", pages = "179-213" } @techreport{gu1991, author = "M. H. Gutknecht", title = "On certain types of $(k,l)$-step methods for solving linear systems of equations", institution = "ETH Z{\"{u}}rich", number = "IPS-91-01", year = "1991" } @article{gu1992, author = "M. H. Gutknecht", title = "A completed theory of the unsymmetric {L}anczos process and related algorithms. {P}art {I}", journal = SIMAX, volume = "13", number = "2", year = "1992", pages = "594-639" } @article{gu1993, author = "M. H. Gutknecht", title = "Changing the norm in conjugate gradient type algorithms", journal = SINUM, volume = "30", year = "1993", pages = "40-56" } @article{gu1993c, author = "M. H. Gutknecht", title = "Variants of {BICGSTAB} for matrices with complex spectrum", journal = SISC, volume = "14", number = "5", year = "1993", pages = "1020-1033" } @article{gu1994, author = "M. H. Gutknecht", title = "A completed theory of the unsymmetric {L}anczos process and related algorithms, {Part II}", journal = SIMAX, volume = "15", year = "1994", pages = "15-58" } @inproceedings{gu1994b, author = "M. H. Gutknecht", title = "The {L}anczos process and {P}adé approximation", booktitle = "Proceedings of the Cornelius Lanczos International Centenary Conference", editor = "J. Brown and M. Chu and D. Ellison and R. J. Plemmons", publisher = "SIAM", year = "1994", pages = "61-75" } @article{gu1997, author = "M. H. Gutknecht", title = "{L}anczos-type solvers for nonsymmetric linear systems of equations", journal = ACTNUM, volume = "6", year = "1997", pages = "271-397" } @article{gs2000, author = "M. H. Gutknecht and Z. Strako{\v{s}}", title = "Accuracy of two three-term and three two-term recurrences for {K}rylov space solvers", journal = SIMAX, volume = "22", number = "1", year = "2000", pages = "213-229" } @article{hlm1991, author = "G. Haase and U. Langer and A. Meyer", title = "Domain decomposition methods with inexact subdomain solvers", journal = NLAA, volume = "1", year = "1991", pages = "27-41" } @article{hac1978, author = "W. Hackbusch", title = "On the multigrid method applied to difference equations", journal = "Computing", volume = "20", year = "1978", pages = "291-306" } @article{hac1980, author = "W. Hackbusch", title = "Convergence of multigrid iterations applied to difference equations", journal = MATCOMP, volume = "34", number = "150", year = "1980", pages = "425-440" } @book{hac1985, author = "W. Hackbusch", title = "Multigrid Methods and Applications", publisher = "Springer", year = "1985" } @article{hac1989, author = "W. Hackbusch", title = "The frequency decomposition multigrid method, Part {I}: {A}pplication to anisotropic equations", journal = NUMAT, volume = "56", year = "1989", pages = "229-245" } @article{hac1992, author = "W. Hackbusch", title = "The frequency decomposition multigrid method, Part {II}: {C}onvergence analysis based on the additive {S}chwarz method", journal = NUMAT, volume = "63", year = "1992", pages = "433-453" } @book{hac1994, author = "W. Hackbusch", title = "Iterative Solution of Large Sparse Systems of Equations", publisher = "Springer", year = "1994" } @book{ht1982, author = "W. Hackbusch and U. Trottenberg", title = "Multigrid Methods", publisher = "Springer", year = "1982", note = "Lecture Notes in Mathematics 960" } @misc{haw1992, author = "W. Hackbusch and G. Wittum", title = "Incomplete decomposition: Algorithms, theory and applications", howpublished = "Notes on Numerical Fluid Mechanics 41, Vieweg", year = "1992" } @inproceedings{hd1994, author = "S. M. Hadfield and T. A. Davis", title = "Potential and achievable parallelism in the unsymmetric-pattern multifrontal {LU} factorization method for sparse matrices", booktitle = "Fifth SIAM Conference on Applied Linear Algebra", publisher = "SIAM", year = "1994" } @techreport{hd1994b, author = "S. M. Hadfield and T. A. Davis", title = "A parallel unsymmetric pattern multifrontal method", institution = "University of Florida", number = "TR–94–028", year = "1994" } @inproceedings{hd1994c, author = "S. M. Hadfield and T. A. Davis", title = "Potential and achievable parallelism in the unsymmetric pattern {LU} factorization method for sparse matrices", booktitle = "Fifth SIAM Conference on Applied Linear Algebra", editor = "j. G. Lewis", year = "1994", pages = "387–391" } @article{had1978, author = "A. Hadjidimos", title = "Accelerated overrelaxation method", journal = MATCOMP, volume = "32", number = "141", year = "1978", pages = "149-157" } @article{hly1980, author = "L. A. Hageman and F. T. Luk and D. M. Young", title = "On the equivalence of certain iterative acceleration methods", journal = SINUM, volume = "17", number = "6", year = "1980", pages = "852-873" } @book{hy1981, author = "L. A. Hageman and D. M. Young", title = "Applied Iterative Methods", publisher = "Academic Press", year = "1981", note = "Reprinted by Dover (2003)" } @article{hag1984, author = "W. W. Hager", title = "Condition estimates", journal = SISSC, volume = "5", number = "2", year = "1984", pages = "311-316" } @techreport{hpr1988, author = "M. Haghoo and W. Proskurowski", title = "Parallel implementation of a domain decomposition method", institution = "University of Southern California", number = "CRI 88-06", year = "1988" } @article{hal1980, author = "S. B. Haley", title = "Solution of band matrix equations by projection-recurrence", journal = LAA, volume = "32", year = "1980", pages = "33-48" } @article{hhn1993, author = "M. Hanke and M. Hochbruck and W. Niethammer", title = "Experiments with {K}rylov subspace methods on a massively parallel computer", journal = "Appl. Math.", volume = "38", year = "1993", pages = "440-451" } @inproceedings{hra1971, author = "F. Harary", title = "Sparse matrices and graph theory", booktitle = "Large Sparse Sets of Linear Equations", editor = "J. K. Reid", publisher = "Academic Press", year = "1971", pages = "139-150" } @article{hrr1986, author = "W. J. Harrod", title = "{LU} decompositions of tridiagonal irreducible {H}-matrices", journal = SIADM, volume = "7", number = "2", year = "1986", pages = "180-187" } @article{hnp1991, author = "M. T. Heath and E. G. Ng and B. W. Peyton", title = "Parallel algorithms for sparse linear systems", journal = SIREV, volume = "33", number = "3", year = "1991", pages = "420-460" } @article{hr1995, author = "M. T. Heath and P. Raghavan", title = "A {C}artesian parallel nested dissection algorithm", journal = SIMAX, volume = "16", number = "1", year = "1995", pages = "235-253" } @techreport{hr1993, author = "M. T. Heath and P. Raghavan", title = "Distributed solution of sparse linear systems", institution = "Dept. of Computer Science, University of Tennessee", number = "UT CS-93-201", year = "1993" } @article{her1988, author = "M. T. Heath and C. H. Romine", title = "Parallel solution of triangular systems on distributed memory multiprocessors", journal = SISSC, volume = "9", number = "3", year = "1988", pages = "558-588" } @article{heg1991, author = "M. Hegland", title = "On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete {LU} factorization", journal = NUMAT, volume = "59", year = "1991", pages = "453-472" } @techreport{hgs1990, author = "M. Hegland and P. E. Saylor", title = "Optimization exercise: block {J}acobi for a model problem", institution = "ETH Z{\"{u}}rich", number = "IPS CD-90-4", year = "1990" } @article{hel1976, author = "D. Heller", title = "Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems", journal = SINUM, volume = "13", year = "1976", pages = "484-496" } @phdthesis{hel1977, author = "D. Heller", title = "Direct and iterative methods for block tridiagonal linear systems", school = "Carnegie-Mellon University", year = "1977" } @article{hel1978, author = "D. Heller", title = "A survey of parallel algorithms in numerical linear algebra", journal = SIREV, volume = "20", number = "4", year = "1978", pages ="740-777" } @inproceedings{hem1980, author = "P. W. Hemker", title = "The incomplete {LU}-decomposition as a relaxation method in multi-grid algorithms", booktitle = "Boundary and Interior Layers - Computational and Asymptotic Methods", editor = "J. J. H. Miller", publisher = "Boole Press", year = "1980", pages = "306-311" } @article{hse1981, author = "H. V. Henderson and S. R. Searle", title = "On deriving the inverse of a sum of matrices", journal = SIREV, volume = "23", number = "1", year = "1981", pages = "53-60" } @article{hl1995b, author = "B. Hendrickson and R. Leland", title = "An improved spectral graph partitioning algorithm for mapping parallel computations", journal = SISC, volume = "16", year = "1995", pages = "452–469" } @article{hwo1994, author = "B. Hendrickson and D. E. Womble", title = "The torus-wrap mapping for dense matrix calculations on massively parallel computers", journal = SISC, volume = "15", number = "5", year = "1994", pages = "1201-1226" } @book{hen1964, author = "P. Henrici", title = "Elements of Numerical Analysis", publisher = "John Wiley", year = "1964" } @inproceedings{hve1989, author = "V. E. Henson", title = "Parallel compact symmetric {FFTs}", booktitle = "Vector and Parallel Computing: {I}ssues in {A}pplied research and {D}evelopment", editor = "J. J. Dongarra and I. S. Duff and P. Gaffney and S. McKee", publisher = "Ellis Horwood", year = "1989", pages = "153-164" } @techreport{hes1954, author = "M. R. Hestenes", title = "The conjugate gradient method for solving linear systems", institution = "National Bureau of Standards", number = "INA 54–11", year = "1954" } @book{hes1980, author = "M. R. Hestenes", title = "Conjugate Direction Methods in Optimization", publisher = "Springer", year = "1980" } @article{hs1952, author = "M. R. Hestenes and E. Stiefel", title = "Methods of conjugate gradients for solving linear systems", journal = JNBS, volume = "49", number = "6", year = "1952", pages = "409-436" } @article{hys1998, author = "M. Heyouni and H. Sadok", title = "On a variable smoothing procedure for {K}rylov subspace methods", journal = LAA, volume = "268", year = "1998", pages = "131-149" } @article{hi1986b, author = "N. J. Higham", title = "Efficient algorithms for computing the condition number of a tridiagonal matrix", journal = SISSC, volume = "7", number = "1", year = "1986", pages = "150-165" } @article{hi1987, author = "N. J. Higham", title = "A survey of condition number estimation for triangular matrices", journal = SIREV, volume = "29", number = "4", year = "1987", pages = "575-596" } @article{hi1989, author = "N. J. Higham", title = "The accuracy of solutions to triangular systems", journal = SINUM, volume = "26", number = "5", year = "1989", pages = "252-265" } @inproceedings{hi1989b, author = "N. J. Higham", title = "How accurate is {G}aussian elimination?", booktitle = "Numerical Analysis 1989", editor = "D. F. Griffiths and G. A. Watson", publisher = "Longman Scientific and Technical", year = "1989", pages = "137-154", note = "Vol. 228, Pitman research notes in mathematics series" } @article{hi1990b, author = "N. J. Higham", title = "Bounding the error in {G}aussian elimination for tridiagonal systems", journal = SIMAX, volume = "11", number = "4", year = "1990", pages = "521-530" } @inproceedings{hi1994b, author = "N. J. Higham", title = "A survey of componentwise perturbation theory in numerical linear algebra", booktitle = "Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics", editor = "W. Gautschi", publisher = "American Mathematical Society", year = "1994", pages = "49-78" } @techreport{hi1995, author = "N. J. Higham", title = "The test matrix toolbox for {M}atlab", institution = "Dept. of Mathematics, University of Manchester", number = "Numerical Analysis 276", year = "1995" } @book{hi1996, author = "N. J. Higham", title = "Accuracy and Stability of Numerical Algorithms", publisher = "SIAM", address = "Philadelphia", year = "1996" } @inproceedings{hi1997, author = "N. J. Higham", title = "Testing linear algebra software", booktitle = "The Quality of Numerical Software: Assessment and Enhancement", editor = "R. Boisvert", publisher = "Chapman and Hall", year = "1997", pages = "109-124" } @book{hi2002, author = "N. J. Higham", title = "Accuracy and Stability of Numerical Algorithms", edition = "2nd", publisher = "SIAM", address = "Philadelphia", year = "2002" } @article{hihi1989, author = "N. J. Higham and D. J. Higham", title = "Large growth factors in {G}aussian elimination with pivoting", journal = SIMAX, volume = "10", number = "2", year = "1989", pages = "155-164" } @article{hihi1992, author = "N. J. Higham and D. J. Higham", title = "Backward error and condition of structured linear systems", journal = SIMAX, volume = "13", number = "1", year = "1992", pages = "162-175" } @article{hip1994, author = "N. J. Higham and A. Pothen", title = "Stability of the partitioned inverse method for parallel solution of sparse triangular systems", journal = SISC, volume = "15", number = "1", year = "1994", pages = "139-148" } @phdthesis{hbk1996, author = "M. Hochbruck", title = "The {P}ad{\'e} table and its relation to certain numerical algorithm", school = "Universitat Tubingen", year = "1996" } @article{hl1998, author = "M. Hochbruck and C. Lubich", title = "Error analysis of {K}rylov methods in a nutshell", journal = SISC, volume = "19", number = "2", year = "1998", pages = "695-701" } @article{hck1965, author = "R. W. Hockney", title = "A fast direct solution of {P}oisson's equation using {F}ourier analysis", journal = JACM, volume = "12", year = "1965", pages = "95-113" } @article{hck1970, author = "R. W. Hockney", title = "The potential calculation and some applications", journal = "Methods Comput. Phys.", volume = "9", year = "1970", pages = "135-211" } @book{hj1988, author = "R. W. Hockney and C. R. Jesshope", title = "Parallel Computers 2", publisher = "Adam Hilger", address = "Bristol", year = "1988" } @article{hmr1973, author = "A. J. Hoffman and M. S. Martin and D. J. Rose", title = "Complexity bounds for regular finite difference and finite element grids", journal = SINUM, volume = "10", number = "2", year = "1973", pages = "364-369" } @article{hoo1976, author = "P. Hood", title = "Frontal solution program for unsymmetric matrices", journal = IJNME, volume = "10", number = "2", year = "1976", pages = "379-399" } @book{ho1953, author = "A. S. Householder", title = "Principles of Numerical Analysis", publisher = "McGraw{-}Hill Book Company", address = "New York", year = "1953" } @article{ho1955b, author = "A. S. Householder", title = "Terminating and nonterminating iterations for solving linear systems", journal = SIAMJ, volume = "3", number = "2", year = "1955", pages = "67-72" } @article{ho1958c, author = "A. S. Householder", title = "The approximate solution of matrix problems", journal = JACM, volume = "5", year = "1958", pages = "204–243" } @article{hop1979, author = "E. N. Houstis and T. S. Papatheodorou", title = "High order fast elliptic equation solver", journal = TOMS, volume = "5", number = "4", year = "1979", pages = "431-441" } @techreport{hu1996, author = "T. Huckle", title = "Efficient computation of sparse approximate inverses", institution = "Institut fur Informatik, Technische Universitat Munchen", number = "TUM-19608", year = "1996" } @techreport{hug1994, author = "T. Huckle and M. Grote", title = "A new approach to parallel preconditioning with sparse approximate inverses", institution = "Computer Science Dept., Stanford University", number = "SCCM-94-03", year = "1994" } @article{hug1997, author = "T. Huckle and M. Grote", title = "Parallel preconditioning with sparse approximate inverses", journal = SISC, volume = "18", number = "3", year = "1997", pages = "838-853" } @article{hlw1983, author = "T. J. R. Hughes and I. Levit and J.Winget", title = "An element-by-element solution algorithm for problems of structural and solid mechanics", journal = CMAME, volume = "36", number = "2", year = "1983", pages = "241-254" } @article{huz1991, author = "L. Hulbert and E. Zmijewski", title = "Limiting communication in parallel sparse {C}holesky factorization", journal = SISSC, volume = "12", number = "5", year = "1991", pages = "1184-1197" } @book{ifr1994, author = "G. Ifrah", title = "Histoire universelle des chiffres", publisher = "Robert Laffont", address = "Paris", year = "1994", note = "English translation: {\it The universal history of numbers: {F}rom prehistory to the invention of the computer}, Wiley, 2000" } @article{ik1979, author = "Y. Ikebe", title = "On inverses of {H}essenberg matrices", journal = LAA, volume = "24", year = "1979", pages = "93-97" } @article{iksn1979, author = "M. Ikeuchi and H. Kobayashi and H. Sawami and H. Niki", title = "On the spectral radius of the {J}acobi iteration matrix for a rectangular region with two different media", journal = JCAM, volume = "5", number = "4", year = "1979", pages = "247-258" } @article{il1988, author = "V. P. {Il'in}", title = "Incomplete factorization methods", journal = "Sov. J. Numer. Anal. Math. Modelling", volume = "3", number = "3", year = "1988", pages = "179-198" } @techreport{irt1993, author = "J. Iliash and T. Rosi and J. Toivanen", title = "Two iterative methods for solving the {S}tokes problem", institution = "Detp. of Mathematics, University of Jyv{\"{a}}skyl{\"{a}}", number = "23/1993", year = "1993" } @article{iss1986, author = "I. C. F. Ipsen and Y. Saad and M. H. Schultz", title = "Complexity of dense linear system solution on a multiprocessor ring", journal = LAA, volume = "77", year = "1986", pages = "205-239" } @article{ir1970, author = "B. M. Irons", title = "A frontal solution program for finite element analysis", journal = IJNME, volume = "2", number = "1", year = "1970", pages = "5-32" } @techreport{ito1984, author = "K. Ito", title = "An iterative method for indefinite systems of linear equations", institution = "ICASE, NASA Langley", number = "84–13", year = "1984" } @article{jbs1986, author = "D. A. H. Jacobs", title = "A generalization of the conjugate gradient method to solve complex systems", journal = IMAJNA, volume = "6", year = "1986", pages = "447-452" } @techreport{jms1987, author = "W. Jalby and U. Meier and A. H. Sameh", title = "The behavior of conjugate gradient based algorithms on a multi vector processor with a memory hierarchy", institution = "University of Illinois", number = "CSRD 607", year = "1987" } @article{jam1993, author = "A. Jameson", title = "Computational algorithms for aerodynamic analysis and design", journal = ANM, volume = "13", year = "1993", pages = "383-422" } @article{jw1977, author = "M. Jankowski and H. Wozniakowski", title = "Iterative refinement implies numerical stability", journal = BITNM, volume = "17", number = "3", year = "1977", pages = "303-311" } @article{jkc1990, author = "C. C. {Jay Kuo} and T. F. Chan", title = "Two color {F}ourier analysis of iterative algorithms for elliptic problems with {Red/BLack} ordering", journal = SISSC, volume = "11", year = "1990", pages = "767-793" } @article{jkc1990b, author = "C. C. {Jay Kuo} and T. F. Chan", title = "Multilevel filtering elliptic preconditioners", journal = SISSC, volume = "11", year = "1990", pages = "403-429" } @article{jkc1992, author = "C. C. {Jay Kuo} and T. F. Chan", title = "Multilevel filtering elliptic preconditioners: extensions to more general elliptic problems", journal = SISSC, volume = "13", year = "1992", pages = "227-243" } @phdthesis{je1982, author = "K. C. Jea", title = "Generalized conjugate gradient acceleration of iterative methods", school = "Center for Numerical Analysis, University of Texas at Austin", note = "Report CNA-176", year = "1982" } @article{jy1983, author = "K. C. Jea and D. M. Young", title = "On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems", journal = LAA, volume = "52", year = "1983", pages = "399-417" } @article{jen1971, author = "A. Jennings", title = "Accelerating the convergence of matrix iterative processes", journal = JIMA, volume = "8", year = "1971", pages = "99-110" } @book{jen1977, author = "A. Jennings", title = "Matrix Computations for Engineers and Scientists", publisher = "John Wiley", year = "1977" } @article{jen1977b, author = "A. Jennings", title = "Influence of the eigenvalue spectrum on the convergence rate of the conjugate gradient method", journal = IMAJ, volume = "20", number ="1", year = "1977", pages = "61-72" } @article{jm1977, author = "A. Jennings and G. M. Malik", title = "Partial elimination", journal = IMAJ, volume = "20", number = "3", year = "1977", pages = "307-316" } @article{jm1978, author = "A. Jennings and G. M. Malik", title = "The solution of sparse linear equations by the conjugate gradient method", journal = IJNME, volume = "12", number = "1", year = "1978", pages = "141-158" } @inproceedings{jt1971, author = "A. Jennings and A. D. Tuff", title = "A direct method for the solution of large sparse symmetric simultaneous equations", booktitle = "Large Sparse Sets of Linear Equations", editor = "J. K. Reid", publisher = "Academic Press", year = "1971", pages = "97-104" } @incollection{jes1984, author = "D. C. Jespersen", title = "Multigrid methods for partial differential equations", booktitle = "Studies in Numerical Analysis", editor = "G. H. Golub", publisher = "Mathematical Association of America", year = "1984", pages = "270-318" } @article{jk1982, author = "J. A. G. Jess and H. G. M. Kees", title = "A data structure for parallel {LU} decomposition", journal = "IEEE Trans. Comput.", volume = "C-31", number = "3", year = "1982", pages = "231-239" } @phdthesis{joh1992, author = "Z. Johan", title = "Data parallel finite element techniques for large-scale computational fluid dynamics", school = "Dept. of Mechanical Engineering, Stanford University", year = "1992" } @book{joh1987, author = "C. Johnson", title = "Numerical Solution of Partial Differential Equations by the Finite Element Method", publisher = "Cambridge University Press", year = "1987" } @article{jcr1982, author = "C. R. Johnson", title = "Inverse {M}-matrices", journal = LAA, volume = "47", year = "1982", pages = "195-216" } @article{jmp1983, author = "O. G. Johnson and C. A. Micchelli and G. Paul", title = "Polynomial preconditioners for conjugate gradient calculations", journal = SINUM, volume = "20", number = "2", year = "1983", pages = "362-376" } @techreport{jol1984, author = "L. Johnsson", title = "Odd-even cyclic reduction on ensemble architectures and the solution of tridiagonal systems of equations", institution = "Yale University", number = "CSD/RR-339", year = "1984" } @article{jol1987, author = "L. Johnsson", title = "Solving tridiagonal systems on ensemble architectures", journal = SISSC, volume = "8", number = "3", year = "1987", pages = "354-392" } @article{joma1990, author = "L. Johnsson and K. K. Mathur", title = "Data structures and algorithms for the finite element method on a data parallel supercomputer", journal = IJNME, volume = "29", year = "1990", pages = "881-908" } @techreport{jol1991, author = "P. Joly", title = "R{\'e}solution de syst{\`e}mes lin{\'e}aires avec plusieurs seconds membres par la m{\'e}thode du gradient conjugu{\'e}", institution = "Lab. d’Analyse Num{\'e}rique, Universit{\'e} Pierre et Marie Curie", number = "R91000", year = "1991" } @article{joe1990, author = "P. Joly and R. Eymard", title = "Preconditioned biconjugate gradient methods for numerical reservoir simulation", journal = JCP, volume = "91", number = "2", year = "1990", pages = "298-309" } @article{jom1993, author = "P. Joly and G. Meurant", title = "Complex conjugate gradient methods", journal = NUMALGO, volume = "4", year = "1993", pages = "379-406" } @article{jpa1994, author = "M. T. Jones and M. L. Patrick", title = "Factoring symmetric indefinite matrices on high-performance architectures", journal = SIMAX, volume = "15", number = "1", year = "1994", pages = "273-283" } @inproceedings{jp1992, author = "M. T. Jones and P. E. Plassmann", title = "Solution of large sparse systems of linear equations in massively parallel applications", booktitle = "Supercomputing 92", editor = "R. Werner", publisher = "IEEE", year = "1992", pages = "551-560" } @techreport{jp1992b, author = "M. T. Jones and P. E. Plassmann", title = "The effect of many color orderings on the convergence of iterative methods", institution = "Math. and Computer Science Div., Argonne National Laboratory", number = "MCS-P292-0292", year = "1992" } @inproceedings{jp1993, author = "M. T. Jones and P. E. Plassmann", title = "The efficient parallel iterative solution of large sparse linear systems", booktitle = "Graph Theory and Sparse Matrix Computations", editor = "J. A. George and J. R. Gilbert and J. W. H. Liu", publisher = "Springer", year = "1993", pages = "229-245" } @article{jp1994, author = "M. T. Jones and P. E. Plassmann", title = "Scalable iterative solution of sparse linear systems", journal = PARCOMP, volume = "20", year = "1994", pages = "753-773" } @techreport{jor1974, author = "T. L. Jordan", title = "Gaussian elimination for dense systems on {STAR} and a new parallel algorithm for diagonally dominant tridiagonal systems", institution = "Los Alamos Scientific Laboratory", number = "LA-5803", year = "1974" } @article{jo1994, author = "W. Joubert", title = "A robust {GMRES}-based adaptive polynomial preconditioning algorithm for nonsymmetric linear systems", journal = SISC, volume = "15", number = "2", year = "1994", pages = "427-439" } @article{joy1987, author = "W. Joubert and D. M. Young", title = "Necessary and sufficient condition for the simplification of generalized conjugate gradient algorithms", journal = LAA, volume = "88", year = "1987", pages = "449-485" } @techreport{ju1995, author = "M. Jung", title = "Parallelization of multigrid methods based on domain decomposition ideas", institution = "Technische Universitat Chemnitz", number = "SPC 95-27", year = "1995" } @techreport{kaa1986, author = "E. F. Kaasschieter", title = "The solution of nonsymmetric linear systems by biconjugate gradients or conjugate gradients squared", institution = "Dept. of Mathematics and Informatics, Delft University of Technology", number = "86-21", year = "1986" } @article{kaa1989, author = "E. F. Kaasschieter", title = "A general finite element preconditioning for the conjugate gradient method", journal = BITNM, volume = "29", number = "4", year = "1989", pages = "824-849" } @article{kaa1988, author = "E. F. Kaasschieter", title = "A practical termination criterion for the conjugate gradient method", journal = BITNM, volume = "28", number = "2", year = "1988", pages = "308-322" } @phdthesis{kaa1990, author = "E. F. Kaasschieter", title = "Preconditioned conjugate gradients and mixed-hybrid finite elements for the solution of potential flow problems", school = "Technische Universiteit Delft", year = "1990" } @inproceedings{kp1976, author = "W. Kahan and B. N. Parlett", title = "How far should you go with the {L}anczos process?", booktitle = "Sparse Matrix Computations", editor = "J. R. Bunch and D. J. Rose", publisher = "Academic Press", year = "1976", pages = "131-144" } @book{kms1989, author = "D. Kahaner and C. B. Moler and S. Nash", title = "Numerical Methods and Software", publisher = "Prentice-Hall", address = "Englewood Cliffs, N.J.", year = "1989" } @article{kas1989, author = "C. Kamath and A. Sameh", title = "A projection method for solving nonsymmetric linear systems on multiprocessors", journal = PARCOMP, volume = "9", number = "3", year = "1989", pages = "291-312" } @techreport{ka1991, author = "R. Karlson", title = "A study of some roundoff effects of the {GMRES} method", number = "Li-TH-MAT-R-1990-11", institution = "Department of Mathematics, Link{\"o}ping University", address = "Sweden", year = "1991" } @inproceedings{kk1995, author = "G. Karypis and V. Kumar", title = "A high performance sparse {C}holesky factorization algorithm for scalable parallel computers", booktitle = "Proceedings Frontiers' 95. The Fifth Symposium on the Frontiers of Massively Parallel Computation", publisher = "IEEE", year = "1995" } @book{kel1995, author = "C. T. Kelley", title = "Iterative methods for linear and nonlinear equations", publisher = "SIAM", year = "1995" } @article{kl1970, author = "B. W. Kernighan and S. Lin", title = "An efficient heuristic procedure for partitioning graphs", journal = "Bell System Tech. J.", volume = "49", number = "2", year = "1970", pages = "291-307" } @article{ker1978, author = "D. S. Kershaw", title = "The incomplete {C}holesky-conjugate gradient method for the iterative solution of systems of linear equations", journal = JCP, volume = "26", number = "1", year = "1978", pages = "43-65" } @article{ker1980, author = "D. S. Kershaw", title = "On the problem of unstable pivots in the incomplete {LU} conjugate gradient method", journal = JCP, volume = "38", year = "1980", pages = "114-123" } @article{key1989, author = "D. E. Keyes", title = "Domain decomposition methods for the parallel computation of reacting flows", journal = CPC, volume = "53", year = "1989", pages = "181-200" } @article{keg1987, author = "D. E. Keyes and W. D. Gropp", title = "A comparison of domain decomposition techniques for elliptic partial differential equations", journal = SISSC, volume = "8", number = "2", year = "1987", pages = "166-202" } @book{kcmsv1992, author = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt Eds.", title = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", publisher = "SIAM", year = "1992" } @book{kex1994, author = "D. E. Keyes and {J. Xu Eds.}", title = "Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition", publisher = "American Mathematical Society", year = "1994" } @misc{kic1997, author = "F. Kickinger", title = "Algebraic multigrid for discrete elliptic second order problems", howpublished = "Report J. Kepler University, Linz", year = "1997" } @article{kin1972, author = "D. R. Kincaid", title = "Norms of successive overrelaxation", journal = MATCOMP, volume = "26", number = "118", year = "1972", pages = "345–357" } @article{koy1986, author = "D. R. Kincaid and T. C. Oppe and D. M. Young", title = "Vector computations for sparse linear systems", journal = SIADM, volume = "7", number = "1", year = "1986", pages = "99-112" } @article{kop1992, author = "L. Yu. Kolotilina and B. Polman", title = "On incomplete block factorization methods of generalized {SSOR} type for {H}-matrices", journal = LAA, volume = "117", year = "1992", pages = "111-136" } @article{kol1979, author = "D. G. Korn and J. J. {Lambiotte Jr.}", title = "Computing the fast {F}ourier transform on a vector computer", journal = MATCOMP, volume = "33", number = "147", year = "1979", pages = "977-992" } @book{kow1984, author = "J. S. {Kowalik Ed.}", title = "High Speed Computation", publisher = "Springer", year = "1984", note = "NATO ASI Series vol. 7" } @article{kps1983, author = "D. Kratzer and S. V. Parter and M. Steuerwalt", title = "Block splittings for the conjugate gradient method", journal = "Comp. and Fluids", volume = "11", number = "4", year = "1983", pages = "255-279" } @article{kri1984, author = "L. B. Krishna", title = "On the convergence of the symmetric successive overrelaxation method", journal = LAA, volume = "56", year = "1984", pages = "185-194" } @article{kul1968, author = "U. Kulisch", title = "{\"{U}}ber regulare zerlegungen von matrizen und einige anwendungen", journal = NUMAT, volume = "11", year = "1968", pages = "444-449" } @article{kp1997, author = "G. Kumfert and A. Pothen", title = "Two improved algorithms for envelope and wavefront reduction", journal = BITNM, volume = "37", number = "3", year = "1997", pages = "559-590" } @article{kuz1988, author = "Y. Kuznetsov", title = "New algorithms for approximate realization of implicit difference schemes", journal = "Sov. J. Numer. Anal. Math. Modelling", volume = "3", number = "2", year = "1988", pages = "99-114" } @article{kuz1989, author = "Y. Kuznetsov", title = "Algebraic multigrid domain decomposition methods", journal = "Sov. J. Numer. Anal. Math. Modelling", volume = "4", year = "1989", pages = "361-392" } @article{kuz1989b, author = "Y. Kuznetsov", title = "Multi-level domain decomposition methods", journal = ANM, volume = "6", year = "1989", pages = "303-314" } @inproceedings{kuz1990, author = "Y. Kuznetsov", title = "Multigrid domain decomposition methods", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1990", pages = "290-313" } @article{kuz1995, author = "Y. Kuznetsov", title = "Efficient iterative solvers for elliptic finite element problems on nonmatching grids", journal = "Russ. J. Numer. Anal. Math. Modeling", volume = "10", year = "1995", pages = "187-211" } @techreport{kmv1993, author = "Y. Kuznetsov and P. Manninen and Y. Vassilevski", title = "On numerical experiments with {Neumann-Neumann} and {Neumann-Dirichlet} domain decomposition preconditioners", institution = "Dept.of Mathematics, University of Jyv{\"{a}}skyl{\"{a}}", number = "3/1993", year = "1993" } @article{lan1950, author = "C. Lanczos", title = "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators", journal = JNBS, volume = "45", year = "1950", pages = "255-282" } @article{lan1952, author = "C. Lanczos", title = "Solution of systems of linear equations by minimized iterations", journal = JNBS, volume = "49", year = "1952", pages = "33-53" } @article{lq1986, author = "U. Langer and W. Queck", title = "On the convergence factor of {U}zawa's algorithm", journal = JCAM, volume = "15", year = "1986", pages = "191-202" } @book{lat1993, author = "P. Lascaux and R. Theodor", title = "Analyse Numérique Matricielle Appliquée à l'Art de l'Ingénieur", publisher = "Masson", year = "1993", note = "Tome 1" } @article{lhkk1979, author = "C. L. Lawson and R. J. Hanson and F. T. Krogh and D. R. Kincaid", title = "Algorithm 539: {B}asic linear algebra subprograms for {F}ortran usage", journal = TOMS, volume = "5", number = "3", year = "1979", pages = "308-325" } @article{leb1972, author = "R. C. {Le Bail}", title = "Use of fast {F}ourier transforms for solving partial differential equations in physics", journal = JCP, volume = "9", year = "1972", pages = "440-465" } @article{let1993, author = "P. {Le Tallec}", title = "{Neumann-Neumann} domain decomposition algorithms for solving {2D} elliptic problems with nonmatching grids", journal = "East-West J. Numer. Math.", volume = "1", number = "2", year = "1993", pages = "129-146" } @article{let1994, author = "P. {Le Tallec}", title = "Domain decomposition methods in computational mechanics", journal = "Comp. Mech. Adv.", volume = "2", year = "1994", pages = "121-220" } @article{ltrv1991, author = "P. {Le Tallec} and Y. H. {De Roeck} and M. Vidrascu", title = "Domain decomposition methods for large linearly elliptic three-dimensional problems", journal = JCAM, volume = "34", year = "1991", pages = "93-117" } @article{ltrv1992, author = "P. {Le Tallec} and Y. H. {De Roeck} and M. Vidrascu", title = "A domain decomposed solver for nonlinear elasticity", journal = CMAME, volume = "99", year = "1992", pages = "187-207" } @inproceedings{ltsv1994, author = "P. {Le Tallec} and T. Sassi and M. Vidrascu", title = "Three-dimensional domain decomposition methods with nonmatching grids and unstructured coarse solvers", booktitle = "Domain Decomposition Methods in Scientific and Engineering Computing, Proceedings of the Seventh International Conference on Domain Decomposition", editor = "D. E. Keyes and J. Xu", publisher = "American Mathematical Society", year = "1994", pages = "61-74" } @article{lew1991, author = "{H.-C. Lee} and A. J. Wathen", title = "On element-by-element preconditioning for general elliptic problems", journal = CMAME, volume = "92", number = "2", year = "1991", pages = "215-229" } @phdthesis{leh1995, author = "R. B. Lehoucq", title = "Analysis and implementation of an implicitly restarted {A}rnoldi iteration", school = "Rice University", address = "Houston, Tx, USA", year = "1995" } @article{les1996, author = "R. B. Lehoucq and D. C. Sorensen", title = "Deflation techniques for an implicitly restarted {A}rnoldi iteration", journal = SIMAX, volume = "17", number = "4", year = "1996", pages = "789-821" } @article{leu1989, author = "M. R. Leuze", title = "Independent set orderings for parallel matrix factorization by {G}aussian elimination", journal = PARCOMP, volume = "10", year = "1989", pages = "177-191" } @article{let1988, author = "R. J. {LeVeque} and L. N. Trefethen", title = "Fourier analysis of the {SOR} iteration", journal = IMAJNA, volume = "8", number = "3", year = "1988", pages = "273-279" } @article{lgr1981, author = "J. G. Lewis and R. G. Grimes", title = "Condition number estimation for sparse matrices", journal = SISSC, volume = "2", year = "1981", pages = "384-388" } @article{lpp1989, author = "J. G. Lewis and B. W. Peyton and A. Pothen", title = "A fast algorithm for reordering sparse matrices for parallel factorization", journal = SISSc, volume = "10", number = "6", year = "1989", pages = "1146-1173" } @article{lre1980, author = "J. G. Lewis and R. G. Rehm", title = "The numerical solution of a non separable elliptic partial differential equation by preconditioned conjugate gradients", journal = JNBS, volume = "85", number = "5", year = "1980", pages = "367-390" } @article{lsi1988, author = "J. G. Lewis and H. D. Simon", title = "The impact of hardware gather/scatter on sparse {G}aussian elimination", journal = SISSC, volume = "9", number = "2", year = "1988", pages = "304-311" } @article{lic1988, author = "G. Li and T. F. Coleman", title = "A parallel triangular solver for a distributed-memory multiprocessor", journal = SISSC, volume = "9", number = "3", year = "1988", pages = "485-502" } @article{lic1989, author = "G. Li and T. F. Coleman", title = "A new method for solving triangular systems on distributed memory message passing multiprocessors", journal = SISSC, volume = "10", number = "2", year = "1989", pages = "382-396" } @inproceedings{lic1984, author = "A. Lichnewsky", title = "Some vector and parallel implementations for preconditioned conjugate gradient algorithms", booktitle = "Proceedings of the NATO Workshop on High-Speed Computations", editor = "J. S. Kowalik", publisher = "NATO ASI Series", year = "1984", pages = "343-359" } @article{lij1993, author = "W. Lichtenstein and L. Johnsson", title = "Block-cyclic dense linear algebra", journal = SISC, volume = "14", number = "6", year = " 1993", pages = "1259-1288" } @article{lkg1982, author = "G. Lindskog", title = "The continued fraction methods for the solution of systems of linear equations", journal = BITNM, volume = "22", number = "4", year = "1982", pages = "519-527" } @inproceedings{lio1987, author = "{P.-L.} Lions", title = "On the {Schwarz} alternating method. {I}", booktitle = "First International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and G. H. Golub and G. A. Meurant and J. P{\'{e}}riaux", publisher = "SIAM", year = "1988", pages = "1-42" } @inproceedings{lio1988, author = "{P.-L.} Lions", title = "On the {Schwarz} alternating method. {II}: {S}tochastic interpretation and orders properties", booktitle = "Proceedings of the Second International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. P{\'{e}}riaux and O. Widlund", publisher = "SIAM", year = "1989", pages = "47-70" } @inproceedings{lio1989, author = "{P.-L.} Lions", title = "On the {Schwarz} alternating method. {III}: {A} variant for nonoverlapping subdomains", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. P{\'{e}}riaux and O. Widlund", publisher = "SIAM", year = "1989", pages = "202-223" } @article{lrt1979, author = "R. J. Lipton and D. J. Rose and R. E. Tarjan", title = "Generalized nested dissection", journal = SINUM, volume = "16", number = "2", year = "1979", pages = "346-358" } @article{lit1980, author = "R. J. Lipton and R. E. Tarjan", title = "Applications of a planar separator theorem", journal = SIC, volume = "9", number = "3", year = "1980", pages = "615-627" } @article{liu1985, author = "J. W. H. Liu", title = "Modification of the minimum degree algorithm by multiple elimination", journal = TOMS, volume = "11", year = "1985", pages = "141-153" } @article{liu1987b, author = "J. W. H. Liu", title = "An adaptive general sparse out-of-core {C}holesky factorization scheme", journal = SISSC, volume = "9", number = "4", year = "1987", pages = "585-599" } @article{liu1987c, author = "J. W. H. Liu", title = "A note on sparse factorization in a paging environment", journal = SISSC, volume = "8", number = "6", year = "1987", pages = "1085-1088" } @article{liu1988, author = "J. W. H. Liu", title = "Equivalent sparse matrix reordering by elimination tree rotations", journal = SISSC, volume = "9", number = "3", year = "1988", pages = "424-444" } @article{liu1989, author = "J. W. H. Liu", title = "Reordering sparse matrices for parallel elimination", journal = PARCOMP, volume = "11", year = "1989", pages = "73-91" } @article{liu1989b, author = "J. W. H. Liu", title = "The minimum degree ordering with constraints", journal = SISSC, volume = "10", number = "6", year = "1989", pages = "1136-1145" } @article{liu1990, author = "J. W. H. Liu", title = "The role of elimination trees in sparse factorization", journal = SIMAX, volume = "11", number = "1", year = "1990", pages = "134-172" } @article{liu1992, author = "J. W. H. Liu", title = "The multifrontal method for sparse matrix solution: {T}heory and practice", journal = SIREV, volume = "34", number = "1", year = "1992", pages = "82-109" } @article{lim1989, author = "J. W. H. Liu and A. Mirzaian", title = "A linear reordering algorithm for parallel pivoting of chordal graphs", journal = SIADM, volume = "2", number = "1", year = "1989", pages = "100-107" } @article{lnp1993, author = "J. W. H. Liu and E. G. Ng and B. W. Peyton", title = "On finding supernodes for sparse matrix computations", journal = SIMAX, volume = "14", number = "1", year = "1993", pages = "242-252" } @article{lis1976, author = "J. W. H. Liu and A. H. Sherman", title = "Comparative analysis of the {Cuthill-McKee} and the reverse {Cuthill-McKee} ordering algorithms for sparse matrices", journal = SINUM, volume = "13", number = "2", year = "1976", pages = "198-213" } @article{lkk1983, author = "R. E. Lord and J. S. Kowalik and S. P. Kumar", title = "Solving linear algebraic equations on an {MIMD} computer", journal = JACM, volume = "30", number = "1", year = "1983", pages = "103-117" } @inproceedings{mar1977, author = "N. K. Madsen and G. H. Rodrigue", title = "Odd even reduction for pentadiagonal matrices", booktitle = "Parallel Computers, Parallel Mathematics", editor = "M. Feilmeier", publisher = "IMACS", year = "1977", pages = "103-105" } @inproceedings{mm1982, author = "J. F. Maitre and F. Musy", title = "The contraction number of a class of two-level methods; an exact evaluation for some finite element subspaces and model problems", booktitle = "Multigrid Methods", editor = "W. Hackbusch and U. Trottenberg", publisher = "Springer", year = "1982", pages = "535-544", note = "Proceedings of the Koln-Porz Conference, Lecture Notes in Mathematics 960" } @article{mm1984, author = "J. F. Maitre and F. Musy", title = "Multigrid methods: convergence theory in a variational framework", journal = SINUM, volume = "21", year = "1984", pages = "657-671" } @article{maj1990, author = "J. Mandel", title = "On block diagonal and {S}chur complement preconditioning", journal = NUMAT, volume = "58", year = "1990", pages = "79-93" } @article{mbv1999, author = "J. Mandel and M. Brezina and P. Van{\v{e}}k", title = "Energy optimization of algebraic multigrid bases", journal = "Computing", volume = "62", number = "3", year = "1999", pages = "205-228" } @article{mmr1988, author = "J. Mandel and S. F. {McCormick} and J. Ruge", title = "An algebraic theory for multigrid methods for variational problems", journal = SINUM, volume = "25", number = "1", year = "1988", pages = "91-110" } @article{man1990, author = "L. Mansfield", title = "On the conjugate gradient solution of the {S}chur complement system obtained from domain decomposition", journal = SINUM, volume = "27", number = "6", year = "1990", pages = "1612-1620" } @article{man1977, author = "T. A. Manteuffel", title = "The {T}chebychev iteration for nonsymmetric linear systems", journal = NUMAT, volume = "28", number = "3", year = "1977", pages = "307-327" } @article{man1978, author = "T. A. Manteuffel", title = "Adaptive procedure for estimating parameters for the nonsymmetric {T}chebychev iteration", journal = NUMAT, volume = "31", number = "2", year = "1978", pages = "183-208" } @inproceedings{man1979, author = "T. A. Manteuffel", title = "The shifted incomplete {C}holesky factorization", booktitle = "Sparse Matrix Proceedings 1978", editor = "I. S. Duff and G. W. Stewart", publisher = "SIAM", year = "1979", pages = "41-61" } @article{man1980, author = "T. A. Manteuffel", title = "An incomplete factorization technique for positive definite linear systems", journal = MATCOMP, volume = "34", number = "150", year = "1980", pages = "473-497" } @article{mao1994, author = "T. A. Manteuffel and J. S. Otto", title = "On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method", journal = NLAA, volume = "1", number = "", year = "1994", pages = "449-475" } @article{mao1993, author = "T. A. Manteuffel and J. S. Otto", title = "Optimal equivalent preconditioners", journal = SINUM, volume = "30", number = "3", year = "1993", pages = "790-812" } @article{map1990, author = "T. A. Manteuffel and S. V. Parter", title = "Preconditioning and boundary conditions", journal = SINUM, volume = "27", number = "3", year = "1990", pages = "656-694" } @incollection{mk1988, author = "G. I. Marchuk and Y. A. Kuznetsov", title = "Approximate algorithms for implicit difference schemes", booktitle = "Analyse Mathématique et Applications, Contributions en l'Honneur de Jacques-Louis Lions", publisher = "Gauthiers-Villars", year = "1988", pages = "357-371" } @article{mkm1986, author = "G. I. Marchuk and Y. A. Kuznetsov and A. M. Matsokin", title = "Fictitious domain and domain decomposition methods", journal = "Sov. J. Numer. Anal. Math. Modelling", volume = "1", year = "1986", pages = "3-35" } @article{mkh1990, author = "G. Markham", title = "Conjugate gradient type methods for indefinite, asymmetric and complex systems", journal = IMAJNA, volume = "10", year = "1990", pages = "155-170" } @article{mark1957, author = "H. M. Markowitz", title = "The elimination form of the inverse and its application to linear programming", journal = "Management Science", volume = "3", number = "3", year = "1957", pages = "255-269" } @article{mro1989, author = "M. Marrakchi and Y. Robert", title = "Optimal algorithms for {G}aussian elimination on an {MIMD} computer", journal = PARCOMP, volume = "12", number = "2", year = "1989", pages = "183-194" } @article{mw1965, author = "R. S. Martin and J. H. Wilkinson", title = "Symmetric decomposition of positive definite band matrices", journal = NUMAT, volume = "7", year = "1965", pages = "355-361" } @article{mw1967, author = "R. S. Martin and J. H. Wilkinson", title = "Solution of symmetric and unsymmetric band equations and the calculations of eigenvectors of band matrices", journal = NUMAT, volume = "9", year = "1967", pages = "279-301" } @article{mrt1980, author = "M. M. Martins", title = "On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix", journal = MATCOMP, volume = "33", number = "152", year = "1980", pages = "1269–1273" } @article{mrt1981, author = "M. M. Martins", title = "Note on irreducible diagonally dominant matrices and the convergence of the {AOR} iterative method", journal = MATCOMP, volume = "37", number = "155", year = "1981", pages = "101-103" } @phdthesis{mtw1989, author = "T. P. Mathew", title = "Domain decomposition and iterative refinement methods for mixed finite element discretizations of elliptic problems", school = "Dept. of Computer Science, Courant Institute of Mathematical Sciences", year = "1989" } @article{mtw1993, author = "T. P. Mathew", title = "Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part {I}: algorithms and numerical results", journal = NUMAT, volume = "65", number = "1", year = "1993", pages = "445-468" } @article{mtw1993b, author = "T. P. Mathew", title = "Schwarz alternating and iterative refinement methods for mixed formulations of elliptic problems, part {II}: {C}onvergence theory", journal = NUMAT, volume = "65", number = "1", year = "1993", pages = "469-492" } @article{mprw1998, author = "T. P. Mathew and P. L. Polyakov and G. Russo and J. Wang", title = "Domain decomposition operator splittings for the solution of parabolic equations", journal = SISC, volume = "19", number = "3", year = "1998", pages = "912-932" } @article{mbv1985, author = "O. A. {McBryan} and E. F. {Van de Velde}", title = "Parallel algorithms for elliptic equations", journal = CPAM, volume = "38", year = "1985", pages = "769-795" } @article{mcc1977, author = "S. F. McCormick", title = "The methods of {K}aczmarz and row orthogonalization for solving linear equations and least squares problems in {H}ilbert space", journal = "Indiana Univ. Math. J.", volume = "26", number = "", year = "1977", pages = "1137-1150" } @article{mcc1982, author = "S. F. McCormick", title = "An algebraic interpretation of multigrid methods", journal = SINUM, volume = "19", year = "1982", pages = "548-560" } @article{mcc1985, author = "S. F. McCormick", title = "Multigrid methods for variational problems: general theory for the {V}-cycle", journal = SINUM, volume = "22", year = "1985", pages = "634-643" } @article{mcc1986, author = "S. F. McCormick", title = "The fast adaptive composite ({FAC}) method for elliptic equations", journal = MATCOMP, volume = "46", year = "1986", pages = "439-456" } @book{mcc1987, author = "S. F. McCormick", title = "Multigrid Methods", publisher = "SIAM", year = "1987" } @book{mcc1988, author = "S. F. {McCormick Ed.}", title = "Multigrid Methods: Theory, Applications, and Supercomputing", publisher = "Marcel Dekker", year = "1988", note = "Lecture Notes in Pure and Applied Mathematics 110" } @book{mcc1989, author = "S. F. McCormick", title = "Multilevel Adaptive Methods for Partial Differential Equations", publisher = "SIAM", year = "1989" } @article{mccr1983, author = "S. F. McCormick and J. W. Ruge", title = "Unigrid for multigrid simulation", journal = MATCOMP, volume = "41", number = "163", year = "1983", pages = "43-62" } @article{mcd1980, author = "B. E. McDonald", title = "The {C}hebychev method for solving nonself-adjoint elliptic equations on a vector computer", journal = JCP, volume = "35", year = "1980", pages = "147-168" } @article{mgm1995, author = "A. McKenney and L. Greengard and A. Mayo", title = "A fast {P}oisson solver for complex geometries", journal = JCP, volume = "118", year = "1995", pages = "348-355" } @article{mei1985, author = "U. Meier", title = "A parallel partition method for solving banded systems of linear equations", journal = PARCOMP, volume = "2", year = "1985", pages = "33-43" } @article{mvdv1977, author = "J. A. Meijerink and H. A. van der Vorst", title = "An iterative solution method for linear systems of which the coefficient matrix is a symmetric {M-}matrix", journal = MATCOMP, volume = "31", number = "137", year = "1977", pages = "148-162" } @article{mvdv1981, author = "J. A. Meijerink and H. A. van der Vorst", title = "Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems", journal = JCP, volume = "44", year = "1981", pages = "134-155" } @article{mel1987, author = "R. G. Melhem", title = "Towards efficient implementation of {PCG} methods on vector supercomputers", journal = IJSA, volume = "1", year = "1987", pages = "70-98" } @article{mel1988, author = "R. G. Melhem", title = "A modified frontal technique suitable for parallel systems", journal = SISSC, volume = "9", number = "2", year = "1988", pages = "289-303" } @article{mel1988b, author = "R. G. Melhem", title = "Parallel solution of linear systems with striped sparse matrices", journal = PARCOMP, volume = "6", year = "1988", pages = "165-184" } @article{mes1977, author = "M. Mesina", title = "Convergence acceleration for the iterative solution of the equations $x=Ax+f$", journal = CMAME, volume = "10", year = "1977", pages = "165-173" } @techreport{gm1983, author = "G. Meurant", title = "The {F}ourier/tridiagonal method for the {P}oisson equation from the point of view of block {C}holesky factorization", institution = "Lawrence Berkeley Laboratory", number = "LBID–764", year = "1983" } @article{gm1984b, author = "G. Meurant", title = "The block preconditioned conjugate gradient method on vector computers", journal = BIT, volume = "24", year = "1984", pages = "623-633" } @article{gm1986, author = "G. Meurant", title = "The conjugate gradient method on supercomputers", journal = "Supercomputer", volume = "13", year = "1986", pages = "9-17" } @article{gm1987, author = "G. Meurant", title = "Multitasking the conjugate gradient method on the {CRAY X-MP/48}", journal = PARCOMP, volume = "5", year = "1987", pages = "267-280" } @inproceedings{gm1988c, author = "G. Meurant", title = "Domain decomposition vs block preconditioning", booktitle = "Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and G. H. Golub and G. Meurant and J. Périaux", publisher = "SIAM", year = "1988", pages = "231-249" } @article{gm1988, author = "G. Meurant", title = "Domain decomposition preconditioners for the conjugate gradient method", journal = "Calcolo", volume = "25", number = "1", year = "1988", pages = "103-119" } @inproceedings{gm1988b, author = "G. Meurant", title = "Incomplete domain decomposition preconditioners for the conjugate gradient method", booktitle = "Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing", editor = "G. H. Rodrigue", publisher = "SIAM", year = "1988", pages = "100-106" } @inproceedings{gm1989c, author = "G. Meurant", title = "Incomplete domain decomposition preconditioners for nonsymmetric problems", booktitle = "Second International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1989", pages = "219-225" } @article{gm1989d, author = "G. Meurant", title = "Domain decomposition methods for partial differential equations on parallel computers", journal = IJSA, volume = "2", number = "4", year = "1989", pages = "5-12" } @inproceedings{gm1989e, author = "G. Meurant", title = "Domain decomposition methods for partial differential equations on parallel computers", booktitle = "Vector and Parallel Computing: {I}ssues in {A}pplied {R}esearch and {D}evelopment", editor = "J. J. Dongarra and I. S. Duff and P. Gaffney and S. McKee", publisher = "Ellis Horwood", year = "1989", pages = "241-253" } @article{gm1989, author = "G. Meurant", title = "Practical use of the conjugate gradient method on parallel supercomputers", journal = CPC, volume = "53", number = "1-3", year = "1989", pages = "467-477" } @article{gm1989f, author = "G. Meurant", title = "Iterative methods for multiprocessor vector computers", journal = "Comp. Phys. Rep.", volume = "11", year = "1989", pages = "51–80" } @incollection{gm1990, author = "G. Meurant", title = "The conjugate gradient method on vector and parallel supercomputers", booktitle = "Computational Techniques and Applications", editor = "W. L. Hogarth and B. J. Noye", publisher = "Hemisphere Publishing Corp.", year = "1990" } @inproceedings{gm1991, author = "G. Meurant", title = "Parallel algorithms for supercomputers", booktitle = "Linear Algebra and Digital Signal Processing", editor = "G. H. Golub and P. {Van Dooren}", publisher = "Springer", year = "1991", pages = "289-318" } @inproceedings{gm1991b, author = "G. Meurant", title = "Numerical experiments with domain decomposition methods for parabolic problems on parallel computers", booktitle = "Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "R. Glowinski and Y. A. Kuznetsov and G. Meurant and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1991", pages = "394-408" } @article{gm1991c, author = "G. Meurant", title = "A domain decomposition method for parabolic problems", journal = ANM, volume = "8", year = "1991", pages = "427-441" } @inproceedings{gm1991d, author = "G. Meurant", title = "Domain decomposition methods for solving large sparse linear systems", booktitle = "Computer Algorithms for Solving Linear Algebraic Equations, the State of the Art", editor = "E. Spedicato", publisher = "Springer", year = "1991", pages = "185-206", note = "NATO ASI F, volume 77" } @article{gm1992, author = "G. Meurant", title = "A review on the inverse of symmetric tridiagonal and block tridiagonal matrices", journal = SIMAX, volume = "13", number = "3", year = "1992", pages = "707-728" } @article{gm1992b, author = "G. Meurant", title = "Os computadores paralelos e o futuro da computacao cientifica", journal = "Boletim da SBMAC", volume = "3", number = "1", year = "1992", pages = "36-52" } @article{gm1997, author = "G. Meurant", title = "The computation of bounds for the norm of the error in the conjugate gradient algorithm", journal = NUMALGO, volume = "16", year = "1997", pages = "77-87" } @misc{mcc1990, author = "G. Meurant and T. F. Chan and P. {Ciarlet Jr.}", title = "Multilevel incomplete {C}holesky preconditioners", howpublished = "Unpublished manuscript", year = "1990" } @article{myp1977, author = "C. D. Meyer and R. J. Plemmons", title = "Convergent powers of a matrix with applications to iterative methods for singular linear systems", journal = SINUM, volume = "14", number = "4", year = "1977", pages = "699-705" } @article{mic1994, author = "P. H. Michielse", title = "Parallel multigrid using {PVM}", journal = "Supercomputer", volume = "10", year = "1994", pages = "10-23" } @article{mivdv1988, author = "P. H. Michielse and H. A. {van der Vorst}", title = "Data transport in {W}ang's partition method", journal = PARCOMP, volume = "7", year = "1988", pages = "87-95" } @article{mcb1990, author = "{J.-C.} Miellou and P. {Cortey-Dumont} and M. Boulbrachene", title = "Perturbation of fixed-point iterative methods", journal = "Adv. Parallel Comput.", volume = "1", year = "1990", pages = "81-122" } @article{mse1990, author = "{J.-C.} Miellou and P. Spiteri and D. J. Evans", title = "Le préconditionnement {SSOR} : une estimation du conditionnement obtenu; optimisation du paramètre de relaxation", journal = CRAS, volume = "311", year = "1990", pages = "817-823" } @article{mcz1981, author = "J. P. Milaszewicz", title = "On criticality and the {Stein-Rosenberg} theorem", journal = SINUM, volume = "18", number = "3", year = "1981", pages = "559-564" } @article{mke1965, author = "K. Miller", title = "Numerical analogs to the {Schwarz} alternating procedure", journal = NUMAT, volume = "7", number = "2", year = "1965", pages = "91-103" } @article{mss1985, author = "N. M. Missirlis", title = "A parallel iterative system solver", journal = LAA, volume = "65", year = "1985", pages = "25-44" } @article{mid1986, author = "G. Mitchison and R. Durbin", title = "Optimal numberings of an {N by N} array", journal = SIADM, volume = "7", number = "4", year = "1986", pages = "571-582" } @article{mor1971, author = "J. Mor{\'e}", title = "Global convergence of {Newton Gauss Seidel} methods", journal = SINUM, volume = "8", year = "1971", pages = "325-336" } @article{mos1944, author = "D. Moskovitz", title = "The numerical solution of {L}aplace's and {P}oisson's equations", journal = QAM, volume = "2", number = "2", year = "1944", pages = "148-163" } @techreport{mkg1978, author = "N. Munksgaard", title = "Solution of general sparse symmetric sets of linear equations", institution = "Numerik Institut, Danmarks Tekniske Hojskole", number = "NI-78-02", year = "1978" } @article{mkg1979, author = "N. Munksgaard", title = "New factorization codes for sparse, symmetric and positive definite matrices", journal =BITNM , volume = "19", number = "1", year = "1979", pages = "43-52" } @article{mkg1980, author = "N. Munksgaard", title = "Solving sparse symmetric sets of linear equations by preconditioned conjugate gradients", journal = TOMS, volume = "6", number = "2", year = "1980", pages = "206-219" } @techreport{muk1987, author = "H. {Munthe-Kaas}", title = "The convergence rate of inexact preconditioned steepest descent algorithm for solving linear systems", institution = "Computer Science Dept., Stanford University", number = "NA–87–04", year = "1987" } @article{nab1999, author = "R. Nabben", title = "Decay rates of the inverse of nonsymmetric tridiagonal and band matrices", journal = SIMAX, volume = "20", number = "3", year = "1999", pages = "820-837" } @phdthesis{na1991, author = "N. M. Nachtigal", title = "A look-ahead variant of the {L}anczos algorithm and its application to the quasi-minimal residual method for non {H}ermitian linear systems", school = "MIT", note = "RIACS Tech. Report 91.19, NASA Ames", year = "1991" } @article{nrtr1992, author = "N. M. Nachtigal and S. C. Reddy and L. N. Trefethen", title = "How fast are nonsymmetric matrix iterations?", journal = SIMAX, volume = "13", number = "3", year = "1992", pages = "778-795" } @article{nrt1992, author = "N. M. Nachtigal and L. Reichel and L. N. Trefethen", title = "A hybrid {GMRES} algorithm for nonsymmetric linear systems", journal = SIMAX, volume = "13", number = "3", year = "1992", pages = "796-825" } @article{nbe1997, author = "A. E. Naiman and I. Babu\v{s}ka and H. C. Elman", title = "A note on conjugate gradient convergence", journal = NUMAT, volume = "76", number = "2", year = "1997", pages = "209-230" } @book{nsh1990, author = "S. G. {Nash Ed.}", title = "A History of Scientific Computing", publisher = "ACM Press", year = "1990" } @techreport{nrs1994, author = "F. Nataf and F. Rogier and E. {de Sturler}", title = "Optimal interface conditions for domain decomposition methods", institution = "Centre de Mathématiques Appliquées, Ecole Polytechnique", number = "RI 301", year = "1994" } @article{npo1992, author = "L. Neal and G. Poole", title = "A geometric analysis of {G}aussian elimination", journal = LAA, volume = "173", year = "1992", pages = "239-264" } @article{nva1980, author = "A. Neumaier and R. S. Varga", title = "Exact convergence and divergence domains for the symmetric successive overrelaxation iterative ({SSOR}) method applied to {H}-matrices", journal = LAA, volume = "58", year = "1980", pages = "261-272" } @article{neu1981, author = "M. Neumann", title = "The {K}ahan {SOR} convergence bound for nonsingular and irreducible {M}-matrices", journal = LAA, volume = "39", year = "1981", pages = "205-222" } @article{npl1987, author = "M. Neumann and R. J. Plemmons", title = "Convergence of parallel multisplitting iterative methods for {M}-matrices", journal = LAA, volume = "88", year = "1987", pages = "559-573" } @article{nev1980, author = "M. Neumann and R. S. Varga", title = "On the sharpness of some upper bounds for the spectral radii of {SOR} iteration matrices", journal = NUMAT, volume = "35", year = "1980", pages = "69-79" } @article{ng1993, author = "E. G. Ng", title = "Supernodal symbolic {C}holesky factorization on a local memory multiprocessor", journal = PARCOMP, volume = "19", year = "1993", pages = "153-162" } @article{ngp1993, author = "E. G. Ng and B. W. Peyton", title = "A supernodal {C}holesky factorization algorithm for shared memory multiprocessors", journal = SISC, volume = "14", number = "4", year = "1993", pages = "761-769" } @article{ngp1993b, author = "E. G. Ng and B. W. Peyton", title = "Block sparse {C}holesky algorithms on advanced uniprocessor computers", journal = SISC, volume = "14", number = "5", year = "1993", pages = "1034-1056" } @article{ni1975, author = "R. A. Nicolaides", title = "On multiple grid and related techniques for solving discrete elliptic systems", journal = JCP, volume = "19", year = "1975", pages = "418-431" } @article{ni1979, author = "R. A. Nicolaides", title = "On some theoretical and practical aspects of multigrid methods", journal = MATCOMP, volume = "33", number = "147", year = "1979", pages = "933-952" } @article{ni1987, author = "R. A. Nicolaides", title = "Deflation of conjugate gradients with applications to boundary value problems", journal = SINUM, volume = "24", number = "2", year = "1987", pages = "355-365" } @article{niv1983, author = "W. Niethammer and R. S. Varga", title = "The analysis of $k$-step iterative methods for linear systems from smmability theory", journal = NUMAT, volume = "41", year = "1983", pages = "177-206" } @article{no1991, author = "Y. Notay", title = "Conditioning analysis of modified block incomplete factorizations", journal = LAA, volume = "154", year = "1991", pages = "711-722" } @article{no1993, author = "Y. Notay", title = "On the convergence rate of the conjugate gradients in presence of rounding errors", journal = NUMAT, volume = "65", number = "1", year = "1993", pages = "301-317" } @techreport{no1993b, author = "Y. Notay", title = "Ordering methods for approximate factorization preconditioning", institution = "Université libre de Bruxelles", number = "IT/IF/14-11", year = "1993" } @article{no1994, author = "Y. Notay", title = "{DRIC}: a dynamic version of the {RIC} method", journal = NLAA, volume = "1", year = "1994", pages = "511-532" } @article{no2000, author = "Y. Notay", title = "Optimal order preconditioning of finite difference matrices", journal = SISC, volume = "21", number = "6", year = "2000", pages = "1991-2007" } @article{no1998, author = "Y. Notay", title = "Optimal {V}-cycle algebraic multilevel preconditioning", journal = NLAA, volume = "5", number = "5", year = "1998", pages = "441-459" } @techreport{nopa1982, author = "B. {Nour-Omid} and B. N. Parlett", title = "Element preconditioning", institution = "University of California, Berkeley", number = "PAM-103", year = "1982" } @article{nopa1985, author = "B. {Nour-Omid} and B. N. Parlett", title = "Element preconditioning using splitting techniques", journal = SISSC, volume = "6", year = "1985", pages = "761-771" } @article{oc1973, author = "M. J. {O'Carroll}", title = "Inconsistencies and {SOR} convergence for the discrete {N}eumann problem", journal = JIMA, volume = "11", year = "1973", pages = "343-350" } @article{oc1976, author = "M. J. {O'Carroll}", title = "Diagonal dominance and {SOR} performance with skew nets", journal = IJNME, volume = "10", year = "1976", pages = "225-240" } @article{op1964, author = "W. Oettli and W. Prager", title = "Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides", journal = NUMAT, volume = "6", number = "1", year = "1964", pages = "405-409" } @article{oga1993, author = "A. T. Ogielski and W. Aiello", title = "Sparse matrix computations on parallel processor arrays", journal = SISC, volume = "14", number = "3", year = "1993", pages = "519-530" } @article{old1940, author = "R. Oldenburger", title = "Infinite powers of matrices and characteristic roots", journal = DUK, volume = "6", number = "2", year = "1940", pages = "357-361" } @article{olst1986, author = "D. P. {O'Leary} and G. W. Stewart", title = "Assignment and scheduling in parallel matrix factorization", journal = LAA, volume = "77", year = "1986", pages = "275-299" } @phdthesis{ol1976, author = "D. P. {O'Leary}", title = "Hybrid conjugate gradient algorithms", school = "Stanford University", year = "1976" } @article{ol1980, author = "D. P. {O'Leary}", title = "Estimating matrix condition numbers", journal = SISSC, volume = "1", number = "2", year = "1980", pages = "205-209" } @article{ol1984, author = "D. P. {O'Leary}", title = "Ordering schemes for parallel processing of certain mesh problems", journal = SISSC, volume = "5", year = "1984", pages = "620-632" } @article{olwh1985, author = "D. P. {O'Leary} and R. E. White", title = "Multisplittings and parallel solution of linear systems", journal = SIADM, volume = "6", number = "4", year = "1985", pages = "630-640" } @article{olw1979, author = "D. P. {O'Leary} and O. B. Widlund", title = "Capacitance matrix methods for the {H}elmholtz equation on general three-dimensional regions", journal = MATCOMP, volume = "33", number = "147", year = "1979", pages = "849-879" } @article{ol1980b, author = "D. P. {O'Leary}", title = "The block conjugate gradient algorithm and related methods", journal = LAA, volume = "29", year = "1980", pages = "293-322" } @techreport{ost1986, author = "J. Oliger and W. Skamarock and W.-P. Tang", title = "Convergence analysis and acceleration of the {S}chwarz alternating method", institution = "Center for Large Scale Scientific Computation, Stanford University", number = "CLaSSiC-86-12", year = "1986" } @article{oli1962, author = "T. A. Oliphant", title = "An extrapolation procedure for solving linear systems", journal = QAM, volume = "20", number = "3", year = "1962", pages = "257-265" } @article{owi1982, author = "F. W. Olver and J. H. Wilkinson", title = "A posteriori error bounds for {G}aussian elimination", journal = JIMA, volume = "2", year = "1982", pages = "377-406" } @article{onhl1984, author = "H. L. Ong", title = "Fast approximate solution of large scale sparse linear systems", journal = JCAM, volume = "10", year = "1984", pages = "45-54" } @phdthesis{ong1989, author = "M. E. Ong", title = "Hierarchical basis preconditioner for second order elliptic problems in three dimensions", school = "Dept. of Applied Mathematics, University of Washington", year = "1989" } @techreport{ong1991, author = "M. E. Ong", title = "Linear hierarchical basis preconditioners in three dimensions", institution = "Dept. of Mathematics, UCLA", number = "CAM 91-15", year = "1991" } @article{ong1997, author = "M. E. Ong", title = "Hierarchical basis preconditioners in three dimensions", journal = SISC, volume = "18", number = "2", year = "1997", pages = "479-498" } @article{os1984, author = "G. Opfer and G. Schober", title = "Richardson's iteration for nonsymmetric matrices", journal = LAA, volume = "58", year = "1984", pages = "343-361" } @book{ort1988, author = "J. M. Ortega", title = "Introduction to Parallel and Vector Solution of Linear Systems", publisher = "Plenum Press", year = "1988" } @article{ort1988b, author = "J. M. Ortega", title = "The ijk forms of factorization methods {I}. {V}ector computers", journal = PARCOMP, volume = "7", number = "2", year = "1988", pages = "135-148" } @article{op1979, author = "J. M. Ortega and R. J. Plemmons", title = "Extensions of the {Ostrowski-Reich} theorem for {SOR} iterations", journal = LAA, volume = "28", year = "1979" } @article{orr1988, author = "J. M. Ortega and C. H. Romine", title = "The ijk forms of factorization methods {II}. {P}arallel systems", journal = PARCOMP, volume = "7", number = "2", year = "1988", pages = "149-162" } @article{ov1985, author = "J. M. Ortega and R. G. Voigt", title = "Solution of partial differential equations on vector and parallel computers", journal = SIREV, volume = "27", number = "2", year = "1985", pages = "149-240" } @incollection{ovr1990, author = "J. M. Ortega and R. G. Voigt and C. H. Romine", title = "A bibliography on parallel and vector numerical algorithms", booktitle = "Parallel Algorithms for Matrix Computations", editor = "K. Gallivan and M. Heath and E. Ng and B. Peyton and R. Plemmons and C. Romine and A. Sameh and R. Voigt", publisher = "SIAM", year = "1990", pages = "125-196" } @book{oz1983, author = "O. {{\O}}sterby and Z. Zlatev", title = "Direct Methods for Sparse Matrices", note = "Lecture notes in computer science 157", publisher = "Springer", year = "1983" } @article{old1994, author = "P. Oswald", title = "On the convergence rate of {SOR}: a worst case estimate", journal = "Computing", volume = "52", year = "1994", pages = "245-255" } @article{pai1974, author = "C. C. Paige", title = "Bidiagonalization of matrices and solution of linear equations", journal = SINUM, volume = "11", number = "1", year = "1974", pages = "197-209" } @article{pai1976, author = "C. C. Paige", title = "Error analysis of the {L}anczos algorithm for tridiagonalizing a symmetric matrix", journal = JIMA, volume = "18", year = "1976", pages = "341-349" } @techreport{ps1973, author = "C. C. Paige and M. A. Saunders", title = "Solution of sparse indefinite systems of linear equations and least squares problems", institution = "Computer Science Dept., Stanford University", number = "STAN-CS-73-399", year = "1973" } @article{ps1975, author = "C. C. Paige and M. A. Saunders", title = "Solution of sparse indefinite systems of linear equations", journal = SINUM, volume = "12", number = "4", year = "1975", pages = "617-629" } @techreport{ps1978, author = "C. C. Paige and M. A. Saunders", title = "A bidiagonalization algorithm for sparse linear equations and least squares problems", institution = "Systems Optimization Lab., Stanford University", number = "SOL 78-19", year = "1978" } @article{psm1975, author = "N. Papamichael and G. D. Smith", title = "The determination of consistent orderings for the {SOR} iterative method", journal = JIMA, volume = "15", year = "1975", pages = "239-248" } @book{par1980, author = "B. N. Parlett", title = "The Symmetric Eigenvalue Problem", publisher = "Prentice Hall", year = "1980", note = "Reprinted by SIAM (1998)" } @article{par1980a, author = "B. N. Parlett", title = "A new look at the {L}anczos algorithm for solving symmetric systems of linear equations", journal = LAA, volume = "29", year = "1980", pages = "323-346" } @article{parr1970, author = "B. N. Parlett and J. K. Reid", title = "On the solution of a system of linear equations whose matrix is symmetric but not definite", journal = BIT, volume = "10", year = "1970", pages = "386-397" } @article{ps1979, author = "B. N. Parlett and D. S. Scott", title = "The {L}anczos algorithm with selective orthogonalization", journal = MATCOMP, volume = "33", number = "145", year = "1979", pages = "217-238" } @article{par1961, author = "S. V. Parter", title = "The use of linear graphs in {G}auss elimination.", journal = SIREV, volume = "3", number = "2", year = "1961", pages = "119-130" } @article{pst1980, author = "S. V. Parter and M. Steuerwalt", title = "On k-line and k x k block iterative schemes for a problem arising in three-dimensional elliptic difference equations", journal = SINUM, volume = "17", number = "6", year = "1980", pages = "823-839" } @article{pst1985, author = "S. V. Parter and M. Steuerwalt", title = "Block iterative methods for elliptic finite element equations", journal = SINUM, volume = "22", number = "1", year = "1985", pages = "146-179" } @article{pmgm1994, author = "G.H. Paulino and I. F. Menezes and M. Gattass and S. Mukherjee", title = "Node and element resequencing using the {L}aplacian of a finite element graph: part {I}- general concepts and algorithm", journal = IJNME, volume = "37", year = "1994", pages = "1511-1530" } @article{pey1967, author = "V. Pereyra", title = "Accelerating the convergence of discretization algorithms", journal = SINUM, volume = "4", number = "4", year = "1967", pages = "508-533" } @article{ppw1977, author = "V. Pereyra and W. Proskurowski and O. B. Widlund", title = "High order {L}aplace solvers for the {D}irichlet problem on general regions", journal = MATCOMP, volume = "31", number = "137", year = "1977", pages = "1-16" } @phdthesis{per1995, author = "O. Perlot", title = "Pr{\'{e}}conditionnements de syst{\`e}mes lin{\'{e}}aires sur machines massivement parall{\`e}les CM-2 et CM-5", school = "Universit{\'{e}} Paris VI", year = "1995" } @article{pkp1979, author = "M. Petravic and G. {Kuo-Petravic}", title = "An {ILUCG} algorithm which minimizes in the {E}uclidean norm", journal = JCP, volume = "32", year = "1979", pages = "263-269" } @phdthesis{pyn1986, author = "B. W. Peyton", title = "Some applications of clique trees to the solution of sparse linear systems", school = "Clemson University", year = "1986" } @book{pi1984, author = "S. Pissanetsky", title = "Sparse Matrix Technology", publisher = "Academic Press", year = "1984" } @article{poo1987, author = "E. L. Poole and J. M. Ortega", title = "Multicolor {ICCG} methods for vector computers", journal = SINUM, volume = "24", number = "6", year = "1987", pages = "1394-1418" } @article{pn1991, author = "G. Poole and L. Neal", title = "A geometric analysis of {G}aussian elimination, {I}", journal = LAA, volume = "149", year = "1991", pages = "249-272" } @article{pn1992, author = "G. Poole and L. Neal", title = "Gaussian elimination: when is scaling beneficial?", journal = LAA, volume = "162", year = "1992", pages = "309-324" } @inproceedings{pot1996, author = "A. Pothen", title = "Graph partitioning algorithms with application to scientific computing", booktitle = "Parallel Numerical Algorithms", editor = "D. E. Keyes and A. H. Sameh and V. Venkatakrishnan", publisher = "Academic Press", year = "1996", pages = "323-368" } @article{poa1992, author = "A. Pothen and F. L. Alvarado", title = "A fast reordering algorithm for parallel sparse triangular solution", journal = SISSC, volume = "13", number = "2", year = "1992", pages = "645-653" } @article{psl1990, author = "A. Pothen and H. D. Simon and K.-P. Liou", title = "Partitioning sparse matrices with eigenvectors of graphs", journal = SIMAX, volume = "11", number = "3", year = "1990", pages = "430-452" } @article{pos1993, author = "A. Pothen and C. Sun", title = "A mapping algorithm for parallel sparse {C}holesky factorization", journal = SISC, volume = "14", number = "5", year = "1993", pages = "1253-1257" } @article{prk1979, author = "W. Proskurowski", title = "Numerical solution of {H}elmholtz's equation by implicit capacitance matrix methods", journal = TOMS, volume = "5", number = "1", year = "1979", pages = "36-49" } @inproceedings{prks1990, author = "W. Proskurowski and S. Sha", title = "Performance of the {Neumann-Dirichlet} preconditioner for substructures with intersecting interfaces", booktitle = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "T. F. Chan and R. Glowinski and J. Périaux and O. B. Widlund", publisher = "SIAM", year = "1990", pages = "322-338" } @article{pw1976, author = "W. Proskurowski and O. B. Widlund", title = "On the numerical solution of {H}elmholtz's equation by the capacitance matrix method", journal = MATCOMP, volume = "30", number = "135", year = "1976", pages = "433-468" } @article{pw1980, author = "W. Proskurowski and O. B. Widlund", title = "A finite element capacitance mattrix method for the {N}eumann problem for {L}aplace's equation", journal = SISSC, volume = "1", number = "4", year = "1980", pages = "410-425" } @article{prz1963, author = "J. S. Przemieniecki", title = "Matrix structural analysis of substructures", journal = "Am. Inst. Aero. Astro. J.", volume = "1", number = "1", year = "1963", pages = "138-147" } @book{prz1968, author = "J. S. Przemieniecki", title = "Theory of Matrix Structural Analysis", publisher = "McGraw-Hill", year = "1968" } @techreport{qu1990, author = "A. Quarteroni", title = "Domain decomposition method for the numerical solution of partial differential equations", institution = "Supercomputer Research Institute, University of Minnesota", number = "UMSI 90/246", year = "1990" } @article{qu1991, author = "A. Quarteroni", title = "Domain decomposition and parallel processing for the numerical solution of partial differential equations", journal = "Surv. Math. Industry", volume = "1", year = "1991", pages = "75-118" } @article{quz1991, author = "A. Quarteroni and E. Zampieri", title = "Finite element preconditioning for {L}egendre spectral collocation approximations to elliptic equations and systems", journal = SINUM, volume = "29", number = "4", year = "1991", pages = "917-936" } @article{rbr1989, author = "G. {Radicati di Brozolo} and Y. Robert", title = "Parallel conjugate gradient like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor", journal = PARCOMP, volume = "11", year = "1989", pages = "223-239" } @article{rag1995, author = "P. Raghavan", title = "Distributed sparse {G}aussian elimination and orthogonal factorization", journal = SISC, volume = "16", number = "6", year = "1995", pages = "1462-1477" } @book{re1971c, author = "J. K. Reid", title = "Proc. Conference on Large Sparse Sets of Linear Equations ", publisher = "Academic Press", address = "New York", year = "1971" } @article{re1971b, author = "J. K. Reid", title = "A note on the stability of {G}aussian elimination", journal = IMAJ, volume = "8", number = "3", year = "1971", pages = "374-375" } @inproceedings{re1971, author = "J. K. Reid", title = "On the method of conjugate gradients for the solution of large sparse systems of linear equations", booktitle = "Proc. Conference on Large Sparse Sets of Linear Equations", editor = "J. K. Reid", publisher = "Academic Press", address = "New York", year = "1971" } @article{re1972, author = "J. K. Reid", title = "The use of conjugate gradients for systems of linear equations possessing ''{P}roperty {A}'' ", journal = SINUM, volume = "9", number = "2", year = "1972", pages = "325-332" } @techreport{re1986, author = "J. K. Reid", title = "Sparse matrices", institution ="Harwell Laboratory" , number = "CSS 201", year = "1986" } @inproceedings{rro1984, author = "E. Reiter and G. H. Rodrigue", title = "An incomplete {C}holesky factorization by a matrix partition algorithm", booktitle = "Elliptic Problem Solvers II", editor = "G. Birkhoff and A. Schoenstadt ", publisher = "Academic Press", year = "1984", pages = "161-173" } @phdthesis{res1990, author = "D. Resasco", title = "Domain decomposition algorithms for elliptic partial differential equations", school = "Dept. of Computer Science, Yale University", year = "1990", note = "YALEU/DCS/RR-776" } @article{reu1996, author = "A. Reusken", title = "A multigrid method based on incomplete {G}aussian elimination", journal = NLAA, volume = "3", number = "5", year = "1996", pages = "369-390" } @book{rim1967, author = "R. D. Richtmyer and K. W. Morton", title = "Difference Methods for Initial-value Problems", edition = "2nd", publisher = "Wiley-Interscience", address = "New York", year = "1967" } @article{rg1967, author = "J. L. Rigal and J. Gaches", title = "On the compatibility of a given solution with the data of a linear system", journal = JACM, volume = "14", number = "3", year = "1967", pages = "543-548" } @article{riz1984, author = "S. A. Rizvi", title = "Inverses of quasi tridiagonal matrices", journal = LAA, volume = "56", year = "1984", pages = "177-184" } @article{rob1969, author = "F. Robert", title = "Blocs {H}-matrices et convergence des méthodes itératives classiques par blocs", journal = LAA, volume = "2", year = "1969", pages = "223-265" } @article{roby1982, author = "Y. Robert", title = "Regular incomplete factorizations of real positive definite matrices", journal = LAA, volume = "48", year = "1982", pages = "105-117" } @article{row1992, author = "P. D. Robinson and A. J. Wathen", title = "Variational bounds on the entries of the inverse of a matrix", journal = IMAJNA, volume = "12", year = "1992", pages = "463-486" } @book{rod1982, author = "G. H. {Rodrigue Ed.}", title = "Parallel Computations", publisher = "Academic Press", year = "1982" } @article{rod1985, author = "G. H. Rodrigue", title = "Inner/outer iterative methods and numerical {S}chwarz algorithms", journal = PARCOMP, volume = "2", year = "1985", pages = "205-218" } @book{rod1989, author = "G. H. {Rodrigue Ed.}", title = "Parallel processing for scientific computing", publisher = "SIAM", year = "1989" } @inproceedings{ros1985, author = "G. H. Rodrigue and P. E. Saylor", title = "Inner/outer iterative methods and numerical {S}chwarz algorithms - {II}", booktitle = "Proceedings of the IBM Conference on Vector and Parallel Computations for Scientific Computing", year = "1985" } @techreport{rosi1984, author = "G. H. Rodrigue and J. Simon", title = "Jacobi splittings and the method of overlapping domains for solving elliptic {PDE}'s", institution = "Lawrence Livermore National Laboratory", number = "UCRL-90656", year = "1984" } @inproceedings{rosi1984b, author = "G. H. Rodrigue and J. Simon", title = "A generalization of the numerical {S}chwarz algorithm", booktitle = "Computing Methods in Applied Sciences and Engineering {VI}", editor = "R. Glowinski and J.-L. Lions", publisher = "North-Holland", year = "1984", pages = "273-283" } @article{row1984, author = "G. H. Rodrigue and D. Wolitzer", title = "Preconditioning by incomplete block cyclic reduction", journal = MATCOMP, volume = "42", number = "166", year = "1984", pages = "549-565" } @article{rmk1979, author = "G. H. Rodrigue and N. K. Madsen and J. I. Karush", title = "Odd-even reduction for banded linear equations", journal = JACM, volume = "26", number = "1", year = "1979", pages = "72-81" } @article{roh1990, author = "J. Rohn", title = "Nonsingularity under data rounding", journal = LAA, volume = "139", year = "1990", pages = "171-174" } @article{rom1985, author = "J. Roman", title = "Calcul de complexit{\'e} relatifs {\`a} une m{\'e}thode de dissection embo{\^\i}t{\'e}e", journal = NUMAT, volume = "47", year = "1985", pages = "175-190" } @article{rom1986, author = "F. Romani", title = "On the additive structure of the inverses of banded matrices", journal = LAA, volume = "80", year = "1986", pages = "131-140" } @article{roo1988, author = "C. H. Romine and J. M. Ortega", title = "Parallel solution of triangular systems of equations", journal = PARCOMP, volume = "6", year = "1988", pages = "109-114" } @article{ros1970, author = "D. J. Rose", title = "Triangulated graphs and the elimination process", journal = JMAA, volume = "32", year = "1970", pages = "597-609" } @article{ros1980, author = "D. J. Rose", title = "Matrix identities of the fast {F}ourier transform", journal = LAA, volume = "29", year = "1980", pages = "423-443" } @article{rt1978, author = "D. J. Rose and R. E. Tarjan", title = "Algorithmic aspects of vertex elimination on directed graphs", journal = SIAP, volume = "34", number = "1", year = "1978", pages = "176-197" } @article{rt1976, author = "D. J. Rose and R. E. Tarjan", title = "Algorithmic aspects of vertex elimination on directed graphs", journal = SIAP, volume = "34", number = "1", year = "1976", pages = "176-197" } @book{rw1972, author = "D. J. Rose and R. A. Willoughby", title = "Sparse Matrices and their Applications", publisher = "Springer", address = "Boston, MA", year = "1972" } @phdthesis{rot1993, author = "E. Rothberg", title = "Exploiting the memory hierarchy in sequential and parallel sparse {C}holesky factorization", school = "Stanford University", year = "1993" } @article{rg1994, author = "E. Rothberg and A. Gupta", title = "An efficient block-oriented approach to parallel sparse {C}holesky factorization", journal = SISC, volume = "15", number = "6", year = "1994", pages = "1413-1439" } @inproceedings{rtd1994, author = "F. X. Roux and D. {Tromeur-Dervout}", title = "Parallelization of a multigrid solver via a domain decomposition method", booktitle = "Domain Decomposition Methods in Scientific and Engineering Computing: Proceedings of the Seventh International Conference on Domain Decomposition", editor = "D. E. Keyes and J. Xu", publisher = "American Mathematical Society", year = "1994", pages = "439-444" } @inproceedings{rs1985, author = "J. W. Ruge and K. St{\"{u}}ben", title = "Efficient solution of finite difference and finite element equations by algebraic multigrid ({AMG})", booktitle = "Multigrid Methods for Integral and Differential Equations", editor = "D. J. Paddon and H. Holstein", publisher = "Clarendon Press", year = "1985", pages = "169-212" } @article{ru1983, author = "A. Ruhe", title = "Numerical aspects of {Gram-Schmidt} orthogonalization of vectors", journal = LAA, volume = "52", year = "1983", pages = "591-601" } @phdthesis{rui1992, author = "D. Ruiz", title = "Solution of large sparse unsymmetric linear systems with a block iterative method in a multiprocessor environment", school = "INPT Toulouse", year = "1992", note = "CERFACS Report TH-PA-92-19649" } @article{sa1981, author = "Y. Saad", title = "{K}rylov subspace methods for solving large nonsymmetric linear systems", journal = MATCOMP, volume = "37", year = "1981", pages = "105-126" } @article{sa1982, author = "Y. Saad", title = "The {L}anczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems", journal = SINUM, volume = "19", number = "3", year = "1982", pages = "470-484" } @article{sa1983, author = "Y. Saad", title = "Iterative solution of indefinite symmetric linear systems by methods using orthogonal polynomials over two disjoint intervals", journal = SINUM, volume = "20", number = "4", year = "1983", pages = "784-811" } @article{sa1985, author = "Y. Saad", title = "Practical use of polynomial preconditionings for the conjugate gradient method", journal = SISSC, volume = "6", number = "4", year = "1985", pages = "865-881" } @article{sa1986, author = "Y. Saad", title = "Communication complexity of the {G}aussian elimination algorithm on multiprocessors", journal = LAA, volume = "77", year = "1986", pages = "315-340" } @article{sa1987b, author = "Y. Saad", title = "On the {L}anczos method for solving symmetric linear systems with several right hand sides", journal = MATCOMP, volume = "48", number = "178", year = "1987", pages = "651-662" } @article{sa1987, author = "Y. Saad", title = " Least squares polynomials in the complex plane and their use for solving nonsymmetric linear systems", journal = SINUM, volume = "24", number = "1", year = "1987", pages = "155-169" } @book{sa1992, author = "Y. Saad", title = "Numerical Methods for Large Eigenvalue Problems", publisher = " Manchester University Press", year = "1992", note = "Revised edition, Classics in Applied Mathematics, SIAM, (2011)" } @article{sa1993, author = "Y. Saad", title = "A flexible inner-outer preconditioned {GMRES} algorithm", journal = JSC, volume = "14", number = "2", year = "1993", pages = "461-469" } @book{sa1996, author = "Y. Saad", title = "Iterative Methods for Sparse Linear Systems", publisher = "PWS Publishing Company", year = "1996", note = "Second edition, SIAM 2003" } @article{ss1985, author = "Y. Saad and M. H. Schultz", title = "Conjugate gradient-like algorithms for solving nonsymmetric linear systems", journal = MATCOMP, volume = "44", number = "170", year = "1985", pages = "417-424" } @article{ss1986, author = "Y. Saad and M. H. Schultz", title = "{GMRES}: a generalized minimum residual algorithm for solving nonsymmetric linear systems", journal = SISSC, volume = "7", number = "3", year = "1986", pages = "856-869" } @article{ss1987, author = "Y. Saad and M. H. Schultz", title = "Parallel direct methods for solving banded linear systems", journal = LAA, volume = "88", year = "1987", pages = "623-650" } @article{ss1989, author = "Y. Saad and M. H. Schultz", title = "Data communication in parallel architectures", journal = PARCOMP, volume = "11", number = "2", year = "1989", pages = "131-150" } @article{sw1996, author = "Y. Saad and K. Wu", title = "{DQGMRES}: A direct quasi-minimal residual algorithm based on incomplete orthogonalization", journal = NLAA, volume = "3", number = "4", year = "1996", pages = "329-343" } @article{sad1999, author = "H. Sadok", title = "{CMRH}: a new method for solving nonsymmetric linear systems based on the {H}essenberg reduction algorithm", journal = NUMALGO, volume = "20", number = "4", year = "1999", pages = "303-321" } @techreport{sad1993, author = "H. Sadok", title = "A unified approach to conjugate gradient algorithms for solving nonsymmetric linear systems", institution = "Université de Lille", number = "ANO ?", year = "1993" } @article{sad2005, author = "H. Sadok", title = "Analysis of the convergence of the minimal and the orthogonal residual methods", journal = NUMALGO, volume = "40", year = "2005", pages = "201-216" } @article{sab1977, author = "A. H. Sameh and R. P. Brent", title = "Solving triangular systems on a parallel computer", journal = SINUM, volume = "14", number = "6", year = "1977", pages = "1101-1113" } @article{sak1978, author = "A. H. Sameh and D. J. Kuck", title = "On stable parallel linear system solvers", journal = JACM, volume = "25", number = "1", year = "1978", pages = "81-91" } @article{sas1986, author = "Y. G. Saridakis", title = "Generalized consistent orderings and the accelerated overrelaxation method", journal = BITNM, volume = "26", number = "3", year = "1986", pages = "369-376" } @article{sas1986b, author = "Y. G. Saridakis", title = "On the analysis of the unsymmetric successive overrelaxation method when applied to p-cyclic matrices", journal = NUMAT, volume = "49", year = "1986", pages = "461–473" } @article{ssy1998, author = "M. A. Saunders and H. D. Simon and E. L. Yip", title = "Two conjugate-gradient-type methods for unsymmetric linear equations", journal = SINUM, volume = "25", number = "4", year = "1988", pages = "927-940" } @article{say1988, author = "P. E. Saylor", title = "Leapfrog variants of iterative methods for linear algebraic equations", journal = JCAM, volume = "24", year = "1988", pages = "169-193" } @article{say1980, author = "P. E. Saylor", title = "Use of the singular value decomposition with the {M}anteuffel algorithm for nonsymmetric linear systems", journal = SISSC, volume = "1", number = "2", year = "1980", pages = "210-222" } @techreport{says1990, author = "P. E. Saylor and R. D. Skeel", title = "Linear iterative solvers for implicit {ODE} methods", institution = "NASA Langley Research Center", number = "ICASE 90-51", year = "1990" } @article{sm1991, author = "P. E. Saylor and D. C. Smolarski", title = "Implementation of an adaptive algorithm for {R}ichardson's method", journal = LAA, volume = "154", number = "1991", year = "1991", pages = "615-646" } @article{scw1995, author = "W. Sch{\"o}nauer and R. Weiss", title = "An engineering approach to generalized conjugate gradient methods and beyond", journal = ANM, volume = "19", number = "3", year = "1995", pages = "175-206" } @article{schr1982, author = "R. Schreiber", title = "A new implementation of sparse {Gaussian} elimination", journal = TOMS, volume = "8", number = "3", year = "1982", pages = "256-276" } @article{schr1984, author = "R. Schreiber", title = "Generalized iterative methods for semidefinite linear systems", journal = LAA, volume = "62", year = "1984", pages = "219-230" } @article{scs1976, author = "U. Schumann and R. A. Sweet", title = "A direct method for the solution of {P}oisson's equation with {N}eumann boundary conditions on a staggered grid of arbitrary size", journal = JCP, volume = "20", number = "2", year = "1976", pages = "171-182" } @article{scs1988, author = "U. Schumann and R. A. Sweet", title = "Fast {F}ourier transforms for direct solution of {P}oisson's equation with staggered boundary conditions", journal = JCP, volume = "75", year = "1988", pages = "123-137" } @article{schz1870, author = "H. A. Schwarz", title = "{\"{U}}ber einen grenz{\"{u}}bergang durch alternierendes verfahren", journal = "Vierteljahrsschrift Naturf. Ges. Z{\"{u}}rich", volume = "15", number = "3", year = "1870", pages = "272-286" } @article{scd1979, author = "D. S. Scott", title = "How to make the {L}anczos algorithm converge slowly", journal = MATCOMP, volume = "33", number = "145", year = "1979", pages = "239-247" } @article{sht1992, author = "J. N. Sharid and R. S. Tuminaro", title = "Sparse iterative algorithm software for large scale {MIMD} machines: an initial discussion and implementation", journal = "Concurrency, Pract. Exp.", volume = "4", year = "1992", pages = "481-497" } @misc{sha1997, author = "Y. Shapira", title = "A multilevel method for sparse linear systems", howpublished = "Report Los Alamos National Laboratory", year = "1997" } @article{sha1999, author = "Y. Shapira", title = "Multigrid for locally refined meshes", journal = SISC, volume = "21", number = "3", year = "1999", pages = "1168-1190" } @article{sho1985, author = "A. Shapiro", title = "Optimal block diagonal $\ell_2$-scaling of matrices", journal = SINUM, volume = "22", number = "1", year = "1985", pages = "81-94" } @article{sh1978, author = "A. H. Sherman", title = "Algorithms for sparse {G}aussian elimination with partial pivoting", journal = TOMS, volume = "4", number = "4", year = "1978", pages = "330-338" } @techreport{swk1994, author = "J. R. Shewchuck", title = "An introduction to the conjugate gradient method without the agonizing pain", institution = "Carnegie Mellon University", number = "CMU–CS–94–125", year = "1994" } @article{shi1978, author = "A. S. L. Shieh", title = "On the convergence of the conjugate gradient method for singular capacitance matrix equations from the {N}eumann problem of the {P}oisson equation", journal = NUMAT, volume = "29", year = "1978", pages = "307-327" } @phdthesis{shd1982, author = "H. D. Simon", title = "The {L}anczos algorithm for solving symmetric linear systems", school = "University of California, Berkeley", address = "USA", year = "1982" } @article{shd1984, author = "H. D. Simon", title = "The {L}anczos algorithm with partial reorthogonalization", journal = MATCOMP, volume = "42", number = "165", year = "1984", pages = "115-142" } @article{shd1984b, author = "H. D. Simon", title = "Analysis of the symmetric {L}anczos algorithm with reorthogonalization methods", journal = LAA, volume = "61", year = "1984", pages = "101-131" } @inproceedings{shd1985, author = "H. D. Simon", title = "Incomplete {LU} preconditioners for conjugate gradient type iterative methods", booktitle = "8th SPE Symposium on Reservoir Simulation", year = "1985", pages = "Paper SPE 13533", note = "Also SPE Reservoir Engineering, 3.01 (1988), 302-306" } @article{sim1991, author = "H. D. Simon", title = "Partitioning of unstructured problems for parallel processing", journal = "Computing systems in engineering", volume = "2", number = "2-3", year = "1991", pages = "135-148" } @article{sk1979, author = "R. D. Skeel", title = "Scaling for numerical stability in {G}aussian elimination", journal = JACM, volume = "26", number = "3", year = "1979", pages = "494-526" } @article{sk1980, author = "R. D. Skeel", title = "Iterative refinement implies numerical stability for {G}aussian elimination", journal = MATCOMP, volume = "35", number = "151", year = "1980", pages = "817-832" } @article{sk1981, author = "R. D. Skeel", title = "Effect of equilibration on residual size for partial pivoting", journal = SINUM, volume = "18", number = "3", year = "1981", pages = "449-455" } @article{sf1993, author = "G. L. G. Sleijpen and D. R. Fokkema", title = "{BiCGstab}($\ell$) for linear equations involving unsymmetric matrices with complex spectrum", journal = ETNA, volume = "11", year = "1993", pages = "11-32" } @techreport{svdv1993, author = "G. L. G. Sleijpen and H. {van der Vorst}", title = "Krylov subspace methods for large linear systems of equations", institution = "Dept. of Mathematics, University of Utrecht", number = "803", year = "1993" } @article{svdv1995b, author = "G. L. G. Sleijpen and H. {van der Vorst}", title = "Maintaining convergence properties of {BiCGstab} methods in finite precision arithmetic", journal = NUMALGO, volume = "10", year = "1995", pages = "203-223" } @article{svdv1995c, author = "G. L. G. Sleijpen and H. {van der Vorst}", title = "An overview of approaches for the stable computation of hybrid {BiCG} methods", journal = "Appl.Numer.Math.", volume = "19", year = "1995", pages = "235-254" } @article{svdv1996, author = "G. L. G. Sleijpen and H. {van der Vorst}", title = "Reliable updated residuals in hybrid {BiCG} methods", journal = "Computing", volume = "56", year = "1996", pages = "141-163" } @article{svf1994, author = "G. L. G. Sleijpen and H. {van der Vorst} and D. R. Fokkema", title = "{BiCGstab}($\ell$) and other hybrid {Bi-CG} methods", journal = NUMALGO, volume = "7", number = "1", year = "1994", pages = "75-109" } @techreport{svm1997, author = "G. L. G. Sleijpen and H. A. {van der Vorst} and J. Modersitzki", title = "The main effects of rounding errors in {K}rylov solvers for symmetric linear systems", institution = "University of Utrecht", number = "1006", year = "1997" } @article{svm2001, author = "G. L. G. Sleijpen and H. A. {van der Vorst} and J. Modersitzki", title = "Differences in the effects of rounding errors in {K}rylov solvers for symmetric indefinite linear systems", journal = "SIMAX", volume = "22", number = "3", year = "2001", pages = "736-751" } @article{slo1986, author = "S. W. Sloan", title = "An algorithm for profile and wavefront reduction of sparse matrices", journal = IJNME, volume = "23", number = "2", year = "1986", pages = "239-251" } @article{smi1991, author = "B. F. Smith", title = "A domain decomposition algorithm for elliptic problems in three dimensions", journal = NUMAT, volume = "60", year = "1991", pages = "219-234" } @inproceedings{smi1992, author = "B. F. Smith", title = "An iterative substructuring algorithm for problems in three dimensions", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "91-98" } @article{smi1992b, author = "B. F. Smith", title = "An optimal domain decomposition preconditioner for the finite element solution of linear elasticity problems", journal = SISSC, volume = "13", year = "1992", pages = "364-378" } @article{smi1993, author = "B. F. Smith", title = "A parallel implementation of an iterative substructuring algorithm for problems in three dimensions", journal = SISC, volume = "14", year = "1993", pages = "406-423" } @book{sbg1996, author = "B. F. Smith and P. E. Bj{{\o}}rstad and W. D. Gropp", title = "Domain Decomposition: {P}arallel Multilevel Methods for Elliptic Partial Differential Equations", publisher = "Cambridge University Press", year = "1996" } @article{smw1990, author = "B. F. Smith and O. B. Widlund", title = "A domain decomposition algorithm using a hierarchical basis", journal = SISSC, volume = "11", year = "1990", pages = "1212-1226" } @article{sms1988, author = "D. C. Smolarski and P. E. Saylor", title = "An optimum iterative method for solving any linear system with a square matrix", journal = BIT, volume = "28", year = "1988", pages = "163-178" } @article{so1989, author = "P. Sonneveld", title = "{CGS}, a fast {L}anczos-type solver for nonsymmetric linear systems", journal = SISSC, volume = "10", number = "1", year = "1989", pages = "36-52" } @article{sor1992, author = "D. C. Sorensen", title = "Implicit application of polynomial filters in a k-step {A}rnoldi method", journal = SIMAX, volume = "13", number = "1", year = "1992", pages = "357-385" } @book{so1940, author = "R. V. Southwell", title = "Relaxation Methods in Engineering Science", publisher = "Oxford University Press", address = "Oxford", year = "1940" } @article{stb1992, author = "S. Stark and A. N. Beris", title = "{LU} decomposition optimized for a parallel computer with a hierarchical memory", journal = PARCOMP, volume = "18", number = "9", year = "1992", pages = "959-972" } @techreport{ske1979, author = "R. G. Steinke", title = "An approximate inversion method for five point difference matrix equations", institution = "Los Alamos Scientific Laboratory", number = "LA-UR-79-162", year = "1979" } @book{ste1973, author = "G. W. Stewart", title = "Introduction to Matrix Computations", publisher = "Academic Press", year = "1973" } @article{st1973, author = "G. W. Stewart", title = "Conjugate direction methods for solving systems of linear equations", journal = NUMAT, volume = "21", number = "4", year = "1973", pages = "285-297" } @article{st1975, author = "G. W. Stewart", title = "The convergence of the method of conjugate gradients at isolated extreme points of the spectrum", journal = NUMAT, volume = "24", year = "1975", pages = "85-93" } @article{st1990, author = "G. W. Stewart", title = "Communication and matrix computations on large message passing systems", journal = PARCOMP, volume = "16", number = "1", year = "1990", pages = "27-40" } @misc{st1991, author = "G. W. Stewart", title = "Maybe we should call it ``{L}agrangian elimination''", howpublished = "Na-net, message of Friday June 21, 1991", year = "1991" } @inproceedings{st1991b, author = "G. W. Stewart", title = "Lanczos and linear systems", booktitle = "Proceedings of the {Cornelius Lanczos} International Centenary Conference (1993)", editor = "J. D. Brown and M. T. Chu and D. C. Ellison and R. J. Plemmons", publisher = "SIAM", year = "1994", pages = "135-139" } @article{st1993b, author = "G. W. Stewart", title = "On the perturbation of {LU, Cholesky and QR} factorizations", journal = SIMAX, volume = "14", number = "4", year = "1993", pages = "1141-1145" } @article{st1995, author = "G. W. Stewart", title = "Gauss, statistics, and {G}aussian elimination", journal = "J. Comput. Graph. Statist.", volume = "4", number = "1", year = "1995", pages = "1-11" } @article{st1997, author = "G. W. Stewart", title = "On the perturbation of {LU} and {C}holesky factors", journal = IMAJNA, volume = "17", number = "1", year = "1995", pages = "1-6" } @article{sta1997, author = "G. W. Stewart", title = "The triangular matrices of {G}aussian elimination and related decompositions", journal = IMAJNA, volume = "17", number = "1", year = "1997", pages = "7-16" } @book{st1998, author = "G. W. Stewart", title = "Matrix Algorithms, volume {I}: {B}asic Decompositions", publisher = "SIAM", address = "Philadelphia", year = "1998" } @book{st2001b, author = "G. W. Stewart", title = "Matrix Algorithms, volume {II}: {E}igensystems", publisher = "SIAM", address = "Philadelphia", year = "2001" } @book{ssu1990, author = "G. W. Stewart and {J.-G.} Sun", title = "Matrix Perturbation Theory", publisher = "Academic Press", address = "New York", year = "1990" } @book{sb1980, author = "J. Stoer and R. Bulirsch", title = "Introduction to Numerical Analysis", publisher = "Springer Verlag", address = "New York", year = "1980" } @article{stn1968, author = "H. L. Stone", title = "Iteraive solution of implicit approximations of multidimensional partial differential equations", journal = SINUM, volume = "5", number = "3", year = "1968", pages = "530-558" } @article{shs1975, author = "H. S. Stone", title = "Parallel tridiagonal equation solvers", journal = TOMS, volume = "1", number = "4", year = "1975", pages = "289-307" } @article{str1991, author = "Z. Strako\v{s}", title = "On the real convergence rate of the conjugate gradient method", journal = LAA, volume = "154-156", year = "1991", pages = "535-549" } @book{str1976, author = "G. Strang", title = "Linear Algebra and its Applications", publisher = "Academic Press", year = "1976" } @article{str1969, author = "V. Strassen", title = "Gaussian elimination is not optimal", journal = NUMAT, volume = "13", number = "4", year = "1969", pages = "354-356" } @article{stw1980, author = "J. C. Strikwerda", title = "Iterative methods for the numerical solution of second order elliptic equations with large first order terms", journal = SISSC, volume = "1", number = "1", year = "1980", pages = "119-130" } @article{stb1983, author = "K. St{\"{u}}ben", title = "Algebraic multigrid ({AMG}): experiences and comparisons", journal = AMC, volume = "13", year = "1983", pages = "419-452" } @inproceedings{stu1982, author = "K. St{\"{u}}ben and U. Trottenberg", title = "Multigrid methods: {F}undamental algorithms, model problem analysis and applications", booktitle = "Multigrid Methods, Proceedings of the Koln-Porz Conference", editor = "W. Hackbusch and U. Trottenberg", note = "Lecture Notes in Mathematics 960", publisher = "Springer", year = "1982", pages = "1-176" } @article{shm1988, author = "D. Sundholm", title = "A block preconditioned conjugate gradient method for solving high order finite element matrix equations", journal = CPC, volume = "49", year = "1988", pages = "409-415" } @article{swa1972, author = "P. N. Swarztrauber", title = "On the numerical solution of the {D}irichlet problem for a region of general shape", journal = SINUM, volume = "9", number = "2", year = "1972", pages = "300-306" } @article{swa1973, author = "P. N. Swarztrauber", title = "The direct solution of the discrete {P}oisson equation on the surface of a sphere", journal = JCP, volume = "15", number = "1", year = "1973", pages = "46-54" } @article{swa1974, author = "P. N. Swarztrauber", title = "A direct method for the discrete solution of separable elliptic equations", journal = SINUM, volume = "11", number = "6", year = "1974", pages = "1136-1150" } @article{swa1977, author = "P. N. Swarztrauber", title = "The methods of cyclic reduction, {F}ourier analysis and the {FACR} algorithm for the discrete solution of {P}oisson's equation on a rectangle", journal = SIREV, volume = "S19", number = "3", year = "1977", pages = "490-501" } @inproceedings{swa1982, author = "P. N. Swarztrauber", title = "Vectorizing the {FFTs}", booktitle = "Parallel Computations", editor = "G. H. Rodrigue", publisher = "Academic Press", year = "1982", pages = "51-84" } @article{swa1984, author = "P. N. Swarztrauber", title = "{FFT} algorithms for vector computers", journal = PARCOMP, volume = "1", year = "1984", pages = "45-63" } @article{sws1973, author = "P. N. Swarztrauber and R. A. Sweet", title = "The direct solution of the discrete {P}oisson equation on a disk", journal = SINUM, volume = "10", number = "5", year = "1973", pages = "900-907" } @article{sws1979, author = "P. N. Swarztrauber and R. A. Sweet", title = "Algorithm 541, efficient {F}ortran subprograms for the solution of separable elliptic partial differential equations", journal = TOMS, volume = "5", number = "3", year = "1979", pages = "352-364" } @article{sws1989, author = "P. N. Swarztrauber and R. A. Sweet", title = "Vector and parallel methods for the direct solution of {P}oisson's equation", journal = JCAM, volume = "27", year = "1989", pages = "241-263" } @article{swe1973, author = "R. A. Sweet", title = "Direct methods for the solution of {P}oisson's equation on a staggered grid", journal = JCP, volume = "12", number = "3", year = "1973", pages = "422-428" } @article{swe1974, author = "R. A. Sweet", title = "A generalized cyclic reduction algorithm", journal = SINUM, volume = "11", number = "3", year = "1974", pages = "506-520" } @article{swe1977, author = "R. A. Sweet", title = "A cyclic reduction algorithm for solving block tridiagonal systems of arbitrary dimension", journal = SINUM, volume = "14", number = "4", year = "1977", pages = "706-720" } @phdthesis{twp1987, author = "{W.-P.} Tang", title = "Schwarz splitting and template operators", school = "Computer Science Dept., Stanford University", year = "1987" } @article{twp1992, author = "{W.-P.} Tang", title = "Generalized {S}chwarz splittings", journal = SISSC, volume = "13", number = "2", year = "1992", pages = "573-595" } @article{tar1971, author = "L. Tartar", title = "Une nouvelle caractérisation des {M}-matrices", journal = "RIRO", volume = "3", year = "1971", pages = "127-128" } @article{tpt1979, author = "C. Temperton", title = "Direct methods for the solution of the discrete {P}oisson equation: {S}ome comparisons", journal = JCP, volume = "31", number = "1", year = "1979", pages = "1-20" } @article{tpt1980, author = "C. Temperton", title = "On the {FACR(l)} algorithm for the discrete {P}oisson equation", journal = JCP, volume = "34", number = "3", year = "1980", pages = "314-329" } @article{tpt1983b, author = "C. Temperton", title = "Self-sorting mixed-radix {Fast Fourier Transforms}", journal = JCP, volume = "52", year = "1983", pages = "1-23" } @article{tpt1983, author = "C. Temperton", title = "A note on prime factor {FFT} algorithms", journal = JCP, volume = "52", year = "1983", pages = "198-204" } @article{tpt1985, author = "C. Temperton", title = "Implementation of a self sorting in place prime factor {FFT} algorithm", journal = JCP, volume = "58", year = "1985", pages = "283-299" } @article{tpt1988, author = "C. Temperton", title = "A self-sorting in-place prime factor real/half-complex {FFT} algorithm", journal = JCP, volume = "75", year = "1988", pages = "199-216" } @article{tpt1991, author = "C. Temperton", title = "Self sorting in place {Fast Fourier Transforms}", journal = SISSC, volume = "12", year = "1991", pages = "808-823" } @article{tpt1992, author = "C. Temperton", title = "A generalized prime factor {FFT} algorithm for any $n=2^p 3^q 5^r$", journal = SISSC, volume = "13", number = "3", year = "1992", pages = "676-686" } @article{tew1967, author = "R. P. Tewarson", title = "The product form of inverses of sparse matrices and graph theory", journal = SIREV, volume = "9", number = "1", year = "1967", pages = "91-99" } @article{tew1970, author = "R. P. Tewarson", title = "Computations with sparse matrices", journal = SIREV, volume = "12", number = "4", year = "1970", pages = "527-543" } @book{tew1973, author = "R. P. Tewarson", title = "Sparse Matrices", publisher = "Academic Press", year = "1973" } @article{tzl1989, author = "T. E. Tezduyar and J. Liou", title = "Grouped element by element iteration schemes for incompressible flow computations", journal = CPC, volume = "53", year = "1989", pages = "441-453" } @article{tym1973, author = "W. F. Tinney and W. S. Meyer", title = "Solution of large sparse systems by ordered triangular factorization", journal = "IEEE Trans. Aut. Control", volume = "18", number = "4", year = "1973", pages = "333-346" } @article{tw1967, author = "W. F. Tinney and J. W. Walker", title = "Direct solutions of sparse network equations by optimally ordered triangular factorization", journal = PIEEE, volume = "55", number = "11", year = "1967", pages = "1801-1809" } @article{tis1987, author = "M. Tismenetsky", title = "A direct method for solving linear systems", journal = "Int. J. Comput. Math.", volume = "22", number = "3-4", year = "1987", pages = " " } @techreport{tis1988, author = "M. Tismenetsky", title = "A nested block preconditioning linear solver", institution = "IBM Israel", number = "88.262", year = "1988" } @techreport{tis1988b, author = "M. Tismenetsky", title = "A robust preconditioning technique for solving large sparse linear systems", institution = "IBM Israel", number = "88.264", year = "1988" } @article{tis1990, author = "M. Tismenetsky", title = "A note on a block preconditioner", journal = "Appl. Math. Lett.", volume = "4", number = "2", year = "1990", pages = "75-79" } @article{tie1986, author = "M. Tismenetsky and I. Efrat", title = "An efficient preconditioning algorithm and its analysis", journal = LAA, volume = "80", year = "1986", pages = "252-256" } @techreport{tie1988, author = "M. Tismenetsky and I. Efrat", title = "A modified generalized minimal residual algorithm for nonsymmetric linear systems", institution = "IBM Israel", number = "88.219", year = "1988" } @phdthesis{ton1990, author = "C. H. Tong", title = "Parallel preconditioned conjugate gradient methods for elliptic partial differential equations", school = "University of California, Los Angeles", year = "1990" } @techreport{ton1992, author = "C. H. Tong", title = "A comparative study of preconditioned {L}anczos methods for non symmetric linear systems", institution = "Sandia National Laboratory", number = "AND91-8240", year = "1992" } @article{tcjk1991, author = "C. H. Tong and T. F. Chan and C. C. {Jay Kuo}", title = "A domain decomposition preconditioner based on a change to a multilevel nodal basis", journal = SISSC, volume = "12", number = "6", year = "1991", pages = "1486-1495" } @article{ty1996, author = "C. H. Tong and Q. Ye", title = "A linear system solver based on a modified {K}rylov subspace method for breakdown recovery", journal = NUMALGO, volume = "12", number = "1", year = "1996", pages = "233-251" } @article{ty2000, author = "C. H. Tong and Q. Ye", title = "Analysis of the finite precision biconjugate gradient algorithm for nonsymmetric linear systems", journal = MATCOMP, volume = "69", year = "2000", pages = "1559-1575" } @book{trjf1973, author = "J. F. Traub", title = "Complexity of Sequential and Parallel Numerical Algorithms", publisher = "Academic Press", year = "1973" } @article{tre1985, author = "L. N. Trefethen", title = "Three mysteries of {G}aussian elimination", journal = "SIGNUM Newsletter", volume = "20", number = "4", year = "1985", pages = "2-5" } @article{tre1997, author = "L. N. Trefethen", title = "Pseudospectra of linear operators", journal = SIREV, volume = "39", number = "3", year = "1997", pages = "383-406" } @article{trs1990, author = "L. N. Trefethen and R. S. Schreiber", title = "Average-case stability of {G}aussian elimination", journal = SIMAX, volume = "11", number = "3", year = "1990", pages = "335-360" } @article{tj1973, author = "A. D. Tuff and A. Jennings", title = "An iterative method for large systems of linear structural equations", journal = IJNME, volume = "7", number = "2", year = "1973", pages = "175-183" } @phdthesis{tu1989, author = "R. S. Tuminaro", title = "Multigrid algorithms on parallel processing systems", school = "Dept.of Computer Science, Stanford University", year = "1989" } @article{tu1992, author = "R. S. Tuminaro", title = "A highly parallel multigrid-like method for the solution of the {E}uler equations", journal = SISSC, volume = "13", number = "1", year = "1992", pages = "88-100" } @article{tuw1993, author = "R. S. Tuminaro and D. E. Womble", title = "Analysis of the multigrid {FMV} cycle on large-scale parallel machines", journal = SISC, volume = "14", number = "5", year = "1993", pages = "1159-1173" } @article{tu1948, author = "A. M. Turing", title = "Rounding{-}off errors in matrix processes", journal = QJMAM, volume = "1", year = "1948", pages = "287-308" } @techreport{un1976, author = "R. Underwood", title = "An approximate factorization procedure based on the block {C}holesky decomposition and its use with the conjugate gradient method", institution = "General Electric", address = "San Jos{\'{e}}, USA", number = "NEDO-11386", year = "1976" } @article{vbw1996, author = "A. {van der Ploeg} and E.F. F. Botta and F. W. Wubs", title = "Nested grids {ILU} decomposition ({NGILU})", journal = JCAM, volume = "66", year = "1996", pages = "515-526" } @article{vds1969, author = "A. {van der Sluis}", title = "Condition numbers and equilibration of matrices", journal = NUMAT, volume = "14", number = "1", year = "1969", pages = "14-23" } @article{vsvv1986, author = "A. {van der Sluis} and H. A. {van der Vorst}", title = "The rate of convergence of conjugate gradients", journal = NUMAT, volume = "48", year = "1986", pages = "543-560" } @article{vsvv1987, author = "A. {van der Sluis} and H. A. {van der Vorst}", title = "The convergence behavior of {R}itz values in the presence of close eigenvalues", journal = LAA, volume = "88", year = "1987", pages = "651-694" } @article{vdv1982, author = "H. van der Vorst", title = "A vectorizable variant of some {ICCG} methods", journal = SISSC, volume = "3", number = "3", year = "1982", pages = "350-356" } @article{vdv1986, author = "H. van der Vorst", title = "Analysis of a parallel solution method for tridiagonal systems", journal = PARCOMP, volume = "5", year = "1986", pages = "303-311" } @article{vdv1986b, author = "H. van der Vorst", title = "The performance of {F}ortran implementations for preconditioned conjugate gradients on vector computers", journal = PARCOMP, volume = "3", year = "1986", pages = "49-58" } @techreport{vdv1986c, author = "H. van der Vorst", title = " {(M)ICCG} for {2D} problems on vector computers", institution = "Data Processing Center, Kyoto University", number = "A-17", year = "1986" } @article{vdv1989, author = "H. van der Vorst", title = "{ICCG} and related methods for 3D problems on vector computers", journal = CPC, volume = "53", number = "1-3", year = "1989", pages = "223-235" } @article{vdv1987b, author = "H. van der Vorst", title = "Large tridiagonal and block tridiagonal linear systems on vector and parallel computers", journal = PARCOMP, volume = "5", year = "1987", pages = "45-54" } @article{vdv1988, author = "H. van der Vorst", title = "Practical aspects of parallel scientific computing", journal = "Fut. Gen. Comp. Sys.", volume = "4", year = "1988", pages = "285-291" } @article{vdv1992, author = "H. {van der Vorst}", title = "{BICGSTAB}: {A} fast and smoothly converging variant of {BI-CG} for the solution of non-symmetric linear systems", journal = SISSC, volume = "13", number = "2", year = "1992", pages = "631-644" } @misc{vdv1993, author = "H. {van der Vorst}", title = "Lecture notes on iterative methods", howpublished = "Mathematical Institute, University of Utrecht", year = "1993" } @misc{vdv1995, author = "H. {van der Vorst}", title = "Parallel iterative solution methods for linear systems arising from discretized {PDE}'s", howpublished = "AGARD-FDP-VKI Workshop Lecture Notes", year = "1995" } @inproceedings{vdvc1996, author = "H. {van der Vorst} and T. F. Chan", title = "Linear systems solver: sparse iterative methods", booktitle = "Parallel Numerical Algorithms", editor = "D. E. Keyes and A. H. Sameh and V. Venkatakrishnan", publisher = "Academic Press", year = "1996", pages = "167-202" } @article{vdvv1993, author = "H. {van der Vorst} and C. Vuik", title = "The superlinear convergence behavior of {GMRES}", journal = JCAM, volume = "48", year = "1993", pages = "327-341" } @article{vdvv1994, author = "H. {van der Vorst} and C. Vuik", title = "{GMRESR}: a family of nested {GMRES} methods", journal = NLAA, volume = "1", number = "4", year = "1994", pages = "369-386" } @misc{vk1995, author = "P. Van{\v{e}}k and J. Krizkova", title = "Two level method on unstructured meshes with convergence rate independent of the coarse space size", howpublished = "University of Colorado, Denver", year = "1995" } @techreport{vmb1994, author = "P. Van{\v{e}}k and J. Mandel and M. Brezina", title = "Algebraic multigrid on unstructured meshes", institution = "UCD/CCM", number = "34", year = "1994" } @article{vmb1996, author = "P. Van{\v{e}}k and J. Mandel and M. Brezina", title = "Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems", journal = "Computing", volume = "56", number = "3", year = "1996", pages = "179-196" } @book{cl1992, author = "C. F. {Van Loan}", title = "Computational Frameworks for the {Fast Fourier Transform}", publisher = "SIAM", year = "1992" } @techreport{vvw1996, author = "R. R. P. {van Nooyen} and C. Vuik and P. Wesseling", title = "Some parallelizable preconditioners for {GMRES}", institution = "Delft University of Technology", number = "96-50", year = "1996" } @techreport{vro1983, author = "J. {Van Rosendale}", title = "Minimizing inner product data dependencies in conjugate gradient iteration", institution = "ICASE, NASA Langley Research Center", number = "TR 172178", year = "1983" } @article{wh1995, author = "S. Vandewalle and G. Horton", title = "Fourier mode analysis of the multigrid waveform relaxation and time parallel multigrid methods", journal = "Computing", volume = "54", year = "1995", pages = "317-330" } @article{var1957, author = "R. S. Varga", title = "A comparison of the successive overrelaxation method and semi-iterative methods using {C}hebyshev polynomials", journal = SIAMJ, volume = "5", number = "2", year = "1957", pages = "39-46" } @article{var1959b, author = "R. S. Varga", title = "Orderings of the successive overrelaxation scheme", journal = PJM, volume = "9", year = "1959", pages = "925-939" } @incollection{var1960, author = "R. S. Varga", title = "Factorization and normalized iterative methods", booktitle = "Boundary Problems in Differential Equations", editor = "R. E. Langer", publisher = "University of Wisconsin Press", address = "Madison", year = "1960", note = "Proceedings of a Symposium conducted by the Mathematics Research Center at the University of Wisconsin, Madison, April 20-22, 1959", pages = "121-142" } @book{var1962, author = "R. S. Varga", title = "Matrix Iterative Analysis", publisher = "Prentice-Hall", address = "Englewood Cliffs, N.J.", year = "1962", note = "A revised and expanded edition was published by Springer in 2000" } @article{varc1981, author = "R. S. Varga and {D.-Y. Cai}", title = "On the {LU} factorization of {M}-matrices", journal = NUMAT, volume = "38", year = "1981", pages = "179-192" } @article{varn1984, author = "R. S. Varga and W. Niethammer and {D.-Y. Cai}", title = "P-cyclic matrices and the symmetric successive overrelaxation method", journal = LAA, volume = "58", year = "1984", pages = "425-439" } @article{vsm1980, author = "R. S. Varga and E. B. Saff and V. Mehrmann", title = "Incomplete factorizations of matrices and connections with {H}-matrices", journal = SINUM, volume = "17", number = "6", year = "1980", pages = "787-793" } @article{vas1992, author = "P. S. Vassilevski", title = "Hybrid {V}-cycle algebraic multilevel preconditioners", journal = MATCOMP, volume = "58", year = "1992", pages = "489-512" } @article{vasl1996, author = "P. S. Vassilevski and R. D. Lazarov", title = "Preconditioning mixed finite element saddle point elliptic problems", journal = NLAA, volume = "3", number = "1", year = "1996", pages = "1-20" } @article{vat1988, author = "S. R. Vatsya", title = "Convergence of conjugate residual-like methods to solve linear equations", journal = SINUM, volume = "25", number = "4", year = "1988", pages = "957-964" } @inproceedings{vi1976, author = "P. K. W. Vinsome", title = "Orthomin, an iterative method for solving sparse sets of simultaneous linear equations", booktitle = "Proceedings of the Fourth SPE Symposium on Numerical Simulation of Reservoir Performance", publisher = "Society of Petroleum Engineers of AIME", year = "1976" } @article{voe1980, author = "V. V. Voevodin", title = "On methods of conjugate direction", journal = "USSR Comput. Math. Phys.", volume = "19", year = "1980", pages = "228-233" } @article{vng1947, author = "J. {von Neumann} and H. H. Goldstine", title = "Numerical inverting of matrices of high order", journal = BAMS, volume = "53", year = "1947", pages = "1021-1099" } @techreport{vu1992, author = "C. Vuik", title = "Further experiences with {GMRESR}", institution = "Faculty of Mathematics, Delft University of Technology", number = "92-12", year = "1992" } @article{vu1995, author = "C. Vuik", title = "New insights in {GMRES}-like methods with variable preconditioners", journal = JCAM, volume = "61", number = "2", year = "1995", pages = "189-204" } @article{wac1963, author = "E. L. Wachspress", title = "Extended application of alternating direction implicit iteration model problem theory", journal = SIAMJ, volume = "11", number = "4", year = "1963", pages = "994-1016" } @article{wa1988, author = "H. F. Walker", title = "Implementation of the {GMRES} method using {H}ouseholder transformations", journal = SISSC, volume = "9", number = "1", year = "1988", pages = "152-163" } @inproceedings{wkl1985, author = "J. R. Wallis and R. P. Kendall and T. E. Little", title = "Constrained residual acceleration of conjugate residual methods", booktitle = "SPE 13536, Reservoir Simulation Symposium, Austin Texas", publisher = "Society of Petroleum Engineers", year = "1985" } @article{wcs1999, author = "W. L. Wan and T. F. Chan and B. Smith", title = "An energy-minimizing interpolation for robust multigrid methods", journal = SISC, volume = "21", number = "4", year = "1999", pages = "1632-1649" } @article{whh1981, author = "H. H. Wang", title = "A parallel method for tridiagonal equations", journal = TOMS, volume = "7", number = "2", year = "1981", pages = "170-183" } @inproceedings{wad1991, author = "H. Watanabe and S. Doi", title = "A comparison of {BiCGSTAB and CGS} methods for convection-diffusion equations", booktitle = "Advances in Numerical Methods for Large Sparse Sets of Linear Systems", editor = "T. Nodera", publisher = "Keio University", year = "1991", pages = "19-26" } @article{wasi1993, author = "A. J. Wathen and D. J. Silvester", title = "Fast iterative solution of stabilised {S}tokes systems, part {I}: using simple diagonal preconditioners", journal = SINUM, volume = "30", number = "3", year = "1993", pages = "630-649" } @inproceedings{wei1966, author = "H. F. Weinberger", title = "A posteriori error bounds in iterative matrix inversion", booktitle = "Numerical Solution of Partial Differential Equations", editor = "J. H. Bramble", publisher = "Academic Press", year = "1966", pages = "153-163" } @article{we1995, author = "R. Weiss", title = "A theoretical overview of {K}rylov subspace methods", journal = ANM, volume = "19", number = "3", year = "1995", pages = "207-233" } @book{we1996, author = "R. Weiss", title = "Parameter-free Iterative Linear Solvers", publisher = "Wiley VCH", year = "1996" } @article{we1982, author = "P. Wesseling", title = "Theoretical and practical aspects of a multigrid method", journal = SISC, volume = "3", year = "1982", pages = "387-407" } @inproceedings{we1982b, author = "P. Wesseling", title = "A robust and efficient multigrid method", booktitle = "Multigrid methods, Proceedings of the Koln-Porz Conference", editor = "W. Hackbusch and U. Trottenberg", note = "Lecture Notes in Mathematics 960", publisher = "Springer", year = "1982", pages = "614-630" } @inproceedings{we1991, author = "P. Wesseling", title = "A survey of {F}ourier smoothing analysis results", booktitle = "Multigrid methods {III}", editor = "W. Hackbusch and U. Trottenberg", note = "International Series of Numerical Mathematics 98", publisher = "Birkh{\"{a}}user", year = "1991", pages = "105-127" } @book{we1992, author = "P. Wesseling", title = "An Introduction to Multigrid Methods", publisher = "John Wiley", year = "1992" } @article{wob1965, author = "O. B. Widlund", title = "On the rate of convergence of an alternating direction implicit method in a non commutative case", journal = MATCOMP, volume = "20", year = "1965", pages = "500-515" } @article{wob1971, author = "O. B. Widlund", title = "On the effects of scaling of the {Peaceman-Rachford} method", journal = MATCOMP, volume = "25", number = "113", year = "1971", pages = "33-41" } @article{wid1978, author = "O. B. Widlund", title = "A {L}anczos method for a class of nonsymmetric systems of linear equations", journal = SINUM, volume = "15", number = "4", year = "1978", pages = "801-812" } @book{wif1962, author = "H. S. Wilf", title = "Mathematics for the Physical Sciences", publisher = "Wiley", year = "1962" } @article{wi1961, author = "J. H. Wilkinson", title = "Error analysis of direct methods of matrix inversion", journal = JACM, volume = "8", year = "1961", pages = "281-330" } @book{wi1965, author = "J. H. Wilkinson", title = "The Algebraic Eigenvalue Problem", publisher = "Oxford University Press", address = "Oxford, UK", year = "1965" } @article{wi1971b, author = "J. H. Wilkinson", title = "Modern error analysis", journal = SIREV, volume = "13", number = "4", year = "1971", pages = "548-568" } @article{wih1985, author = "J. M. Winger and T. J. Hughes", title = "Solution algorithms for nonlinear transient heat conduction analysis employing element by element iterative strategies", journal = CMAME, volume = "52", year = "1985", pages = "711-815" } @inproceedings{wys1980, author = "Y. S. Wong", title = "Preconditioned conjugate gradient methods for large sparse matrix problems", booktitle = "Numerical Methods in Thermal Problems", editor = "R. W. Mewis and K. Morgan", publisher = "Pineridge Press", year = "1980", pages = "967-979" } @article{woz1980, author = "H. Wo{\'{z}}niakowski", title = "Roundoff-error analysis of a new class of conjugate-gradient algorithms", journal = LAA, volume = "29", year = "1980", pages = "507-529" } @article{wr1991, author = "S. J. Wright", title = "Parallel algorithms for banded linear systems", journal = SISSC, volume = "12", number = "4", year = "1991", pages = "824-842" } @article{wr1993, author = "S. J. Wright", title = "A collection of problems for which {G}aussian elimination with partial pivoting is unstable", journal = SISC, volume = "14", number = "4", year = "1993", pages = "231-238" } @phdthesis{xuj1989, author = "J. Xu", title = "Theory of multilevel methods", school = "Penn State University", year = "1989" } @article{xuj1992, author = "J. Xu", title = "A new class of iterative methods for nonselfadjoint or indefinite problems", journal = SINUM, volume = "29", year = "1992", pages = "303-319" } @inproceedings{xuj1992b, author = "J. Xu", title = "Iterative methods by {SPD} and small subspace solvers for nonsymmetric or indefinite problems", booktitle = "Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations", editor = "D. E. Keyes and T. F. Chan and G. Meurant and J. S. Scroggs and R. G. Voigt", publisher = "SIAM", year = "1992", pages = "106-118" } @article{xuj1992c, author = "J. Xu", title = "Iterative methods by space decomposition and subspace correction: a unifying approach", journal = SIREV, volume = "34", year = "1992", pages = "581-613" } @article{xuj1996, author = "J. Xu", title = "The auxiliary space method and optimal multigrid preconditioning techniques for unstructured meshes", journal = "Computing", volume = "56", year = "1996", pages = "215-235" } @article{xuc1992, author = "J. Xu and X.-C. Cai", title = "A preconditioned {GMRES} method for nonsymmetric or indefinite problems", journal = MATCOMP, volume = "59", number = "200", year = "1992", pages = "311-319" } @article{xuq1994, author = "J. Xu and J. Qin", title = "Some remarks on a multigrid preconditioner", journal = SISC, volume = "15", year = "1994", pages = "172-184" } @article{yik1979, author = "T. Yamamoto and Y. Ikebe", title = "Inversion of band matrices", journal = LAA, volume = "24", year = "1979", pages = "105-111" } @article{ywh1977, author = "W. H. Yang", title = "A method for updating {C}holesky factorization of a band matrix", journal = CMAME, volume = "12", year = "1977", pages = "281-288" } @article{yan1981, author = "M. Yannakakis", title = "Computing the minimum fill-in is {NP}-complete", journal = SIADM, volume = "2", number = "1", year = "1981", pages = "77-79" } @article{ye1994, author = "Q. Ye", title = "A breakdown-free variation of the nonsymmetric {L}anczos algorithms", journal = MATCOMP, volume = "62", number = "205", year = "1994", pages = "179-207" } @book{yo1971, author = "D. M. Young", title = "Iterative Solution of Large Linear Systems", publisher = "Academic Press", year = "1971", note = "Reprinted by Dover (2003)" } @article{yo1977, author = "D. M. Young", title = "On the accelerated {SSOR} method for solving large linear systems", journal = "Advances in Maths.", volume = "23", year = "1977", pages = "215-271" } @article{yf1963, author = "D. M. Young and T. G. Frank", title = "A survey of computer methods for solving elliptic and parabolic partial differential equations", journal = "ICC Bulletin", volume = "2", number = "1", year = "1963", pages = "3-61" } @article{yj1980, author = "D. M. Young and K. C. Jea", title = "Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods", journal = LAA, volume = "34", year = "1980", pages = "159-194" } @article{ys1986, author = "H. Yserentant", title = "On the multilevel splitting of finite element spaces", journal = NUMAT, volume = "49", year = "1986", pages = "379-412" } @article{ys1986b, author = "H. Yserentant", title = "On the multilevel splitting of finite element spaces for indefinite elliptic boundary value problems", journal = SINUM, volume = "23", year = "1986", pages = "581-595" } @article{ys1986c, author = "H. Yserentant", title = "The convergence of multilevel methods for solving finite element equations in the presence of singularities", journal = MATCOMP, volume = "47", year = "1986", pages = "399-409" } @article{ys1986d, author = "H. Yserentant", title = "Hierarchical bases give conjugate gradient type methods a multigrid speed of convergence", journal = "Appl. Math. Comp.", volume = "19", year = "1986", pages = "347-358" } @article{ys1989, author = "H. Yserentant", title = "Preconditioning indefinite discretization matrices", journal = NUMAT, volume = "54", number = "6", year = "1989", pages = "719-734" } @article{ys1990, author = "H. Yserentant", title = "Two preconditioners based on the multilevel splitting of finite element spaces", journal = NUMAT, volume = "58", year = "1990", pages = "163-184" } @article{zel1992, author = "G. Zhang and H. C. Elman", title = "Parallel sparse {C}holesky factorization on a shared memory multiprocessor", journal = PARCOMP, volume = "18", number = "9", year = "1992", pages = "1009-1022" } @article{zhx1992, author = "X. Zhang", title = "Multilevel {S}chwarz methods", journal = NUMAT, volume = "63", year = "1992", pages = "521-539" } @article{zw1994, author = "L. Zhou and H. F. Walker", title = "Residual smoothing techniques for iterative methods", journal = SISC, volume = "15", year = "1994", pages = "297-312" } @article{zlo1985, author = "O. C. Zienkiewicz and R. Lohner", title = "Accelerated relaxation or direct solution? {F}uture prospects for {FEM}", journal = IJNME, volume = "21", year = "1985", pages = "1-11" } @article{zl1980, author = "Z. Zlatev", title = "On some pivotal strategies in {Gaussian} elimination by sparse technique", journal = SINUM, volume = "17", number = "1", year = "1980", pages = "18-30" } @article{zmg1988, author = "E. Zmijzwski and J. R. Gilbert", title = "A parallel algorithm for sparse symbolic {C}holesky factorization on a multiprocessor", journal = PARCOMP, volume = "7", year = "1988", pages = "199-210" } @article{zyv1986, author = "G. Zyvoloski", title = "Incomplete factorization for finite element methods", journal =IJNME , volume = "23", year = "1986", pages = "1101-1109" }