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Brezinski", title = "Rational approximation to formal power series", journal = JAT, volume = "25", year = "1979", pages = "295-317" } @book{br1980, author = "C. Brezinski", title = "Pad{\'{e}}-type Approximation and General Orthogonal Polynomials", volume = "ISNM 50", publisher = "Birkh{\"a}user, Basel", year = "1980" } @inproceedings{br1985, author = "C. Brezinski", title = "{Edmond Nicolas Laguerre}", booktitle = "Polyn{\^o}mes Orthogonaux et Applications", editor = "C. Brezinski and A. Draux and A. P. Magnus and P. Maroni and A. Ronveaux", publisher = "Springer-Verlag", address = "Heidelberg", year = "1985", pages ="xxi-xxvi", note = "Lecture Notes in Mathematics, vol. 1171" } @article{br1988, author = "C. Brezinski", title = "Other manifestations of the {Schur} complement", journal = LAA, volume = "111", year = "1988", pages = "231-247" } @article{br1990, author = "C. Brezinski", title = "A direct proof of the {Christoffel-Darboux} identity and its equivalence to the recurrence relationship", journal = JCAM, volume = "32", year = "1990", pages = "17-25" } @inproceedings{br1991b, author = {C. Brezinski}, booktitle = {Contributions in Numerical Mathematics}, title = {Biorthogonality and conjugate gradient-type algorithms}, year = {1991}, editor = {R. P. Agarwal}, pages = {55-70}, publisher = {World Scientific}, } @book{br1991, author = "C. Brezinski", title = "History of Continued Fractions and Pad\'{e} Approximants", publisher = "Springer-Verlag", address ="Berlin", year = "1991" } @book{br1992, author = "C. Brezinski", title = "Biorthogonality and its Applications to Numerical Analysis", publisher = "Marcel Dekker", address = "New York", year = "1992" } @article{br1992b, author = "C. Brezinski", title = "A unified approach to various orthogonalities", journal = "Annales de la Facult{\'e} des Sciences de Toulouse: Math{\'e}matiques", volume = "1", number = "3", year = "1992", pages = "277-292" } @techreport{br1995, author = {C. Brezinski}, title = {Hybrid procedures and semi-iterative methods for linear systems}, year = {1995}, number = {?}, institution = {Universit{\'e} de Lille}, } @article{br1996, author = "C. Brezinski", title = "The methods of {Vorobyev} and {Lanczos}", journal = LAA, volume = "234", year = "1996", pages = "21-41" } @article{br1996b, author = "C. Brezinski", title = "Extrapolation algorithms and {Pad{\'e}} approximations: a historical survey", journal = ANM, volume = "20", number = "3", year = "1996", pages = "299-318" } @article{br1997, author = "C. Brezinski", title = "A transpose-free {Lanczos}/{Orthodir} algorithm for linear systems", journal = CRAS, volume = "324", year = "1997", pages = "349-354" } @book{br1997b, author = "C. Brezinski", title = "Projection Methods for Systems of Equations", publisher = "North-Holland", address = "Amsterdam", year = "1997" } @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{br1999, author = "C. Brezinski", title = "Error estimates for the solution of linear systems", journal = SISC, volume = "21", number = "2", year = "1999", pages = "764-781" } @article{br1999b, author = "C. Brezinski", title = "{Krylov} subspace methods, biorthogonal polynomials and {Pad{\'e}}-type approximants", journal = NUMALGO, volume = "21", year = "1999", pages = "97-107" } @article{br1999c, author = "C. Brezinski", title = "Multiparameter descent methods", journal = LAA, volume = "296", number = "1-3", year = "1999", pages = "113-141" } @article{br2000, author = "C. Brezinski", title = "The block {Lanczos} and {Vorobyev} methods", journal = CRAS, volume = "331", year = "2000", pages = "137-142" } @inproceedings{br2002, author = "C. Brezinski", title = "Formal orthogonal polynomials", booktitle = "Computational Aspects of Linear Control", publisher = "Springer", address = "Boston, MA", year = "2002", pages = "73-85" } @techreport{br2002b, author = "C. Brezinski", title = "An introduction to formal orthogonality and some of its applications", institution = "Universit{\'e} de Lille, France", number = "ANO438", year = "2002" } @article{br2003, author = "C. Brezinski", title = "A tribute", journal = NUMALGO, volume = "33", number = "1", year = "2003", pages = "3-9" } @article{br2005, author = "C. Brezinski", title = "La m{\'{e}}thode de {Cholesky}", journal = RHM, volume = "11", year = "2005", pages = "205-238" } @article{br2006, author = "C. Brezinski", title = "The life and work of {Andr\'{e} Cholesky}", journal = NUMALGO, volume = "43", year = "2006", pages = "279-288" } @book{br2006b, author = "C. Brezinski", title = "Histoires de Sciences. Inventions, D{\'e}couvertes et Savants", publisher = "L'Harmattan", address = "Paris", year = "2006" } @article{br2010, author = "C. Brezinski", title = "From numerical quadrature to {Pad{\'e}} approximation", journal = ANM, volume = "60", number = "12", year = "2010", pages = "1209-1220" } @book{br2010b, author = "C. Brezinski", title = "Les Images de la Terre. Cosmographie, G{\'e}od{\'e}sie, Topographie et Cartographie {\`a} Travers les Si{\`e}cles", publisher = "L'Harmattan", address = "Paris", year = "2010" } @article{br2019, author = "C. Brezinski", title = "Reminiscences of {Peter Wynn}", journal = NUMALGO, volume = "80", number = "1", year = "2019", pages = "5-10" } @article{brci2022, author = "C. Brezinski and P. G. Ciarlet", title = "{Richard Steven Varga}, 1928-2022", journal = NUMALGO, volume = "90", year = "2022", pages = "1-2" } @article{bcrs2021, author = "C. Brezinski and S. Cipolla and M. Redivo-Zaglia and Y. Saad", title = "Shanks and {A}nderson-type acceleration techniques for systems of nonlinear equations", journal = IMAJNA, volume = "drab061", year = "2021" } @article{bfm2012, author = "C. Brezinski and P. Fika and M. Mitrouli", title = "Estimations of the trace of powers of positive self-adjoint operators by extrapolation of the moments", journal = ETNA, volume = "39", year = "2012", pages = "144-155" } @article{bfm2012b, author = "C. Brezinski and P. Fika and M. Mitrouli", title = "Moments of a linear operator, with applications to the trace of the inverse of matrices and the solution of equations", journal = NLAA, volume = "19", number = "6", year = "2012", pages = "937-953" } @article{bgc2005, author = {C. Brezinski and M. {Gross-Cholesky}}, journal = {Bull. Soc. Amis. Bib. \'Ec. Polytech.}, title = {La vie et les travaux d'{Andr\'e-Louis Cholesky}}, year = {2005}, pages = {7-32}, volume = {39}, } @book{bmrz2022, author = "C. Brezinski and G. Meurant and M. {Redivo-Zaglia}", title = "A Journey Through the History of Numerical Linear Algebra", publisher = "SIAM", year = "2022" } @article{bnrz2021, author = "C. Brezinski and F. A. Norman and M. Redivo-Zaglia", title = "The Legacy of {Peter Wynn}", journal = "Mathematics", volume = "9", number = "11", year = "2021", pages = "1240-1285" } @article{bnorz2012, author = "C. Brezinski and P. Novati and M. Redivo-Zaglia", title = "A rational {Arnoldi} approach for ill-conditioned linear systems", journal = JCAM, volume = "236", number = "8", year = "2012", pages = "2063-2077" } @article{brra2007, author = "C. Brezinski and M. Raydan", title = "Cauchy-{Schwarz} and {Kantorovich} type inequalities for scalar and matrix moment sequences", journal = ADCM, volume = "26", number = "1", year = "2007", pages = "71-80" } @inproceedings{brz1994c, author = "C. Brezinski and M. Redivo-Zaglia", title = "Breakdowns in the computation of orthogonal polynomials", booktitle = "Nonlinear Numerical Methods and Rational Approximation, {II}", editor = "A. Cuyt", publisher = "Kluwer", address = "Dordrecht", year = "1994", pages = "49-59" } @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{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{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{brz1998, author = "C. Brezinski and M. Redivo-Zaglia", title = "Transpose-free {Lanczos}-type algorithms for nonsymmetric linear systems", journal = NUMALGO, volume = "17", year = "1998", pages = "67-103" } @techreport{brz1999, author = {C. Brezinski and M. Redivo-Zaglia}, title = {On the choice of the auxiliary vectors in {Lanczos}' method for linear systems}, year = {1999}, address = {France}, number = {ANO-402}, institution = {Universit{\'e} de Lille}, } @Article{brz2000, author = {C. Brezinski and M. Redivo-Zaglia}, journal = CALC, title = {Variations on {Lanczos}' tridiagonalization process}, year = {2000}, pages = {159-179}, volume = {37}, } @article{brz2003, author = "C. Brezinski and M. Redivo-Zaglia", title = "A {Schur} complement approach to a general extrapolation algorithm", journal = LAA, volume = "368", year = "2003", pages = "279-301" } @article{brz2006, author = "C. Brezinski and M. Redivo-Zaglia", title = "The {PageRank} vector: properties, computation, approximation, and acceleration", journal = SIMAX, volume = "28", number = "2", year= "2006", pages = "551-575" } @article{brz2013, author = "C. Brezinski and M. Redivo-Zaglia", title = "Pad{\'e}-type rational and barycentric interpolation", journal = NUMAT, volume = "125", number = "1", year = "2013", pages = "89-113" } @article{brz2015, author = "C. Brezinski and M. Redivo-Zaglia", title = "Convergence acceleration of {Kaczmarz}'s method", journal = "J. Eng. Math.", volume = "93", year = "2015", pages = "3-19" } @article{brz2015b, author = "C. Brezinski and M. Redivo-Zaglia", title = "New representations of {Pad{\'e}}, {Pad{\'e}}-type, and partial {Pad{\'e}} approximants", journal = JCAM, volume = "284", year = "2015", pages = "69-77" } @article{brz2019, author = "C. Brezinski and M. Redivo-Zaglia", title = "The genesis and early developments of {A}itken's process, {Shanks} transformation, the $\varepsilon$-algorithm, and related fixed point methods", journal = NUMALGO, volume = "80", year = "2019", pages = "11-133" } @book{brz2020, author = "C. Brezinski and M. Redivo-Zaglia", title = "Extrapolation and rational approximation. {T}he works of the main contributors", publisher = "Springer Nature", address = "Switzerland", year = "2020" } @article{brz2020b, author = "C. Brezinski and M. Redivo-Zaglia", title = "Some unusual results on extrapolation methods", journal = NUMALGO, volume = "84", number = "4", year = "2020", pages = "1241-1264" } @article{brz2023, author = "C. Brezinski and M. Redivo-Zaglia", title = "On the kernel of vector $\varepsilon$-algorithm and related topics", journal = NUMALGO, volume = "92", number = "1", year = "2023", pages = "207-221" } @article{brz2023b, author = "C. Brezinski and M. Redivo-Zaglia", title = "Reuben {Louis Rosenberg} (1909-1986) and the {Stein-Rosenberg} theorem", journal = ETNA, volume = "58", year = "2023", pages = "A1-A38" } @article{brrs1998, author = "C. Brezinski and M. Redivo-Zaglia and G. Rodriguez and S. Seatzu", title = "Extrapolation techniques for ill-conditioned linear systems", journal = NUMAT, volume = "81", number = "1", year = "1998", pages = "1-29" } @article{brrs2003, author = "C. Brezinski and M. Redivo-Zaglia and G. Rodriguez and S. Seatzu", title = "Multi-parameter regularization techniques for ill-conditioned linear systems", journal = NUMAT, volume = "94", number = "2", year = "2003", pages = "203-228" } @article{brsa2018, author = "C. Brezinski and M. Redivo-Zaglia and Y. Saad", title = "Shanks sequence transformations and {A}nderson acceleration", journal = SIREV, volume = "60", number = "3", year = "2018", pages = "646-669" } @article{brs1991, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "Avoiding breakdown and near-breakdown in {Lanczos} type algorithms", journal = NUMALGO, volume = "1", year = "1991", pages = "261-284" } @article{brs1992, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "A breakdown-free {Lanczos} type algorithm for solving linear systems", journal = NUMAT, volume = "63", year = "1992", pages = "29-38" } @article{brs1991b, author = {C. Brezinski and M. Redivo-Zaglia and H. Sadok}, journal = NUMALGO, title = {Addendum to ``{A}voiding breakdown and near-breakdown in {Lanczos} type algorithms''}, year = {1992}, pages = {133-136}, volume = {2}, } @article{brs1997, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "Breakdowns in the implementation of the {Lanczos} method for solving linear systems", journal = CMA, volume = "33", number = "1", year = "1997", pages = "31-44" } @misc{brs1998, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "Problems of breakdown and near-breakdown in {Lanczos}-based algorithms", howpublished = "NATO ASI Series C Mathematical and Physical Sciences-Advanced Study Institute 508", year = "1998", pages = "255-270" } @article{brs1999, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "New look-ahead {Lanczos}-type algorithms for linear systems", journal = NUMAT, volume = "83", number = "1", year = "1999", pages = "53-85" } @article{brs2000, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "The matrix and polynomial approaches to {Lanczos}-type algorithms", journal = JCAM, volume = "123", number = "1-2", year = "2000", pages = "241-260" } @article{brs2002, author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok", title = "A review of formal orthogonality in {Lanczos}-based methods", journal = JCAM, volume = "140", number = "1", year = "2002", pages = "81-98" } @article{brse2008, author = "C. Brezinski and G. Rodriguez and S. Seatzu", title = "Error estimates for linear systems with applications to regularization", journal = NUMALGO, volume = "49", number = "1-4", year = "2008", pages = "85-104" } @article{brse2009, author = "C. Brezinski and G. Rodriguez and S. Seatzu", title = "Error estimates for the regularization of least squares problems", journal = NUMALGO, volume = "51", number = "1", year = "2009", pages = "61-76" } @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{bsrz1994, author = "C. Brezinski and H. Sadok and M. Redivo-Zaglia", title = "Orthogonal polynomials and the {Lanczos} method", journal = "Banach Center Publications", volume = "29", number = "1", year = "1994", pages = "19-33" } @book{brt2014, author = "C. Brezinski and D. Tourn{\`e}s", title = "Andr{\'{e}}{-}{L}ouis {Cholesky} (1875-1918), {M}athematician, {T}opographer and {A}rmy {O}fficer", publisher = "Birkh{\"a}user", address = "Basel", year = "2014" } @book{bt2014, author = "C. Brezinski and D. Tourn{\`e}s", title = "{Andr{\'e}-Louis Cholesky}, mathematician, topographer and army officer", publisher = "Birkh{\"a}user", year = "2014" } @inproceedings{bw2001, author = "C. Brezinski and L. Wuytack", title = "Numerical analysis in the twentieth century", booktitle = "Numerical analysis: {H}istorical Developments in the 20th Century", editor = "C. Brezinski and L. Wuytack", publisher = "North-Holland", address = "Amsterdam", year = "2001", pages = "1-40" } @article{blss2007, author = "F. Brezzi and K. Lipnikov and M. Shashkov and V. Simoncini", title = "A new discretization methodology for diffusion problems on generalized polyhedral meshes", journal = CMAME, volume = "196", number = "37-40", year = "2007", pages = "3682-3692" } @article{bsv2012, author = "M. Briani and A. Sommariva and M. Vianello", title = "Computing {Fekete} and {Lebesgue} points: simplex, square, disk", journal = JCAM, volume = "236", number = "9", year = "2012", pages = "2477-2486" } @article{bck1961, author = "L. Brickman", title = "On the field of values of a matrix", journal = PAMS, volume = "12", number = "1", year = "1961", pages ="61-66" } @article{brha2000, author = "D. Bridges and R. Havea", title = "A constructive analysis of a proof that the numerical range is convex", journal = "LMS J. Comput. Math.", volume = "3", year = "2000", pages = "191-206" } @article{brgr2006, author = "R. Bridson and C. Greif", title = "A multipreconditioned conjugate gradient algorithm", journal = SIMAX, volume = "27", number = "4", year = "2006", pages = "1056-1068" } @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" } @book{bhmc2000, author = "W. L. Briggs and V. E. Henson and S. F. McCormick", title = "A Multigrid Tutorial", edition = "2nd", publisher = "SIAM", year = "2000" } @article{brp1998, author = "S. Brin and L. Page", title = "The anatomy of a large-scale hypertextual web search engine", journal = "Comput. Networks ISDN Syst.", volume = "30", year = "1998", pages = "107-117" } @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}, year = {1985}, number = {71}, institution = {Catholic University of Nijmegen}, } @book{bri1854b, author = "F. Brioschi", title = "La Teorica dei Determinanti e le sue Principali Applicazioni", publisher = "Bizzoni", year = "1854" } @article{bri1854, author = "F. Brioschi", title = "Note sur un th{\'{e}}or{\`e}me relatif aux d{\'{e}}terminants gauches", journal = JMPA, volume = "19", year = "1854", pages = "253-256" } @book{bri1856, author = "F. Brioschi", title = "Th{\'{e}}orie des D{\'{e}}terminants et leurs Principales Applications", publisher = "Mallet-Bachelier", address = "Paris", year = "1856" } @article{bgp1987, author = "M. O. Bristeau and R. Glowinski and J. P{\'e}riaux", title = "Numerical methods for the {Navier-Stokes} equations", journal = CPR, volume = "6", year = "1987", pages = "73-187" } @article{brbu2007, author = "C. Brittin and M. I. Bueno", title = "Numerical properties of shifted tridiagonal {LU} factorizations", journal = MJM, volume = "4", number = "3", year = "2007", pages = "277-290" } @article{brgr2002, author = "O. Br{\"{o}}ker and M. J. Grote", title = "Sparse approximate inverse smoothers for geometric and algebraic multigrid", journal = ANM, volume = "41", number = "1", year = "2002", pages = "61-80" } @article{bs1956, author = "R. A. Brooker and F. H. Sumner", title = "The method of {Lanczos} for calculating the characteristic roots and vectors of a real symmetric matrix", journal = "Proc. Instn. Elect. Engrs B.", volume = "103", year = "1956", pages = "114-119" } @article{brks2006, author = "B. P. Brooks", title = "The coefficients of the characteristic polynomial in terms of the eigenvalues and the elements of an $n\times n$ matrix", journal = AML, volume = "19", number = "6", year = "2006", pages = "511-515" } @inproceedings{batd2020, author = "C. Brown and A. Abdelfattah and S. Tomov and J. J. Dongarra", title = "Design, optimization, and benchmarking of dense linear algebra algorithms on {AMD GPUs}", booktitle = "IEEE High Performance Extreme Computing Conference", publisher = "IEEE", year = "2020", pages = "1-7" } @article{brsp2004, author = "E. S. Brown and I. M. Spitkovsky", title = "On flat portions on the boundary of the numerical range", journal = LAA, volume = "390", year = "2004", pages = "75-109" } @article{brow1991, author = "P. N. Brown", title = "A theoretical comparison of the {Arnoldi} and {GMRES} algorithms", journal = SISSC, volume = "12", number = "1", year = "1991", pages = "58-78" } @article{bh1989, author = "P. N. Brown and A. C. Hindmarsh", title = "Reduced storage matrix methods in stiff {ODE} systems", journal = AMC, volume = "31", year = "1989", pages = "40-91" } @article{bw1997, author = "P. N. Brown and H. F. Walker", title = "{GMRES} on (nearly) singular systems", journal = SIMAX, volume = "18", number = "1", year = "1997", pages = "37-51" } @article{bro1930, author = "E. T. Browne", title = "The characteristic roots of a matrix", journal = BAMS, volume = "36", number = "10", year = "1930", pages = "705-710" } @article{bro1939, author = "E. T. Browne", title = "Limits to the characteristic roots of a matrix", journal = AMM, volume = "46", number = "5", year = "1939", pages = "252-265" } @article{bdghm2000, author = "S. Browne and J. Dongarra and N. Garner and G. Ho and P. Mucci", title = "A portable programming interface for performance evaluation on modern processors", journal = IJHSC, volume = "14", number = "3", year = "2000", pages = "189-204" } @article{bry1964, author = "C. G. Broyden", title = "Some generalisations of the theory of successive over-relaxation", journal = NUMAT, volume = "6", number = "1", year = "1964", pages = "269-284" } @article{bry1973, author = "C. G. Broyden", title = "Some condition number bounds for the {Gauss}ian elimination process", journal = JIMA, volume = "12", year = "1973", pages = "273-286" } @incollection{bry1991, author = "C. G. Broyden", title = "Classical methods for linear equations", booktitle = "Computer Algorithms for Solving Linear Algebraic Equations. NATO ASI Series, vol 77", editor = "E. Spedicato", publisher = "Springer", year = "1991", pages = "1-26", note = "NATO ASI F, volume 77" } @article{brfo1999, author = "C. G. Broyden and P. Foschi", title = "Duality in conjugate gradient methods", journal = NUMALGO, volume = "22", year = "1999", pages = "113-128" } @article{brve2001, author = "C. G. Broyden and M. T. Vespucci", title = "On the convergence of {Krylov} linear equation solvers", journal = OMS, volume = "16", number = "1-4", year = "2001", pages = "113-129" } @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{rr1989, 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", number = "2", year = "1989", pages = "223-239" } @article{bcmm2003, author = "R. Bru and J. Cerd{\'a}n and J. Mar{\'\i}n and J. Mas", title = "Preconditioning sparse nonsymmetric linear systems with the {Sherman-Morrison} formula", journal = SIMAX, volume = "25", number = "2", year = "2003", pages = "701-715" } @article{ben1988, author = "R. Bru and L. Elsner and M. Neumann", title = "Models of parallel chaotic iteration methods", journal = LAA, volume = "103", year = "1988", pages ="175-192" } @article{bgha2012, author = "R. Bru and I. Gim{\'e}nez and A. 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Srako{\v{s}}", title = "70 years of {Krylov} subspace methods: {T}he journey continues", howpublished = "ArXiv preprint, arXiv:2211.00953", year ="2022" } @article{clr2021, author = "E. C. Carson and K. Lund and M. Rozlo\v{z}n{\'\i}k", title = "The stability of block variants of classical {Gram-Schmidt}", journal = SIMAX, volume = "42", number = "3", year = "2021", pages = "1365-1380" } @article{crstt2018, author = "E. C. Carson and M. Rozlo\v{z}n{\'\i}k and Z. Strako\v{s} and P. Tich{\'y} and M. T{\r u}ma", title = "The numerical stability analysis of pipelined conjugate gradient methods: Historical context and methodology", journal = SISC, volume = "40", number = "5", year = "2018", pages = "A3549-A3580" } @article{cast2020, author = "E. C. Carson and Z. Strako\v{s}", title = "On the cost of iterative computations", journal = "Philos. Trans. Royal Soc. A", volume = "378", number = "2166", year = "2020", pages = "20190050" } @article{ctn1991, author = "C. Carstensen", title = "Inclusion of the roots of a polynomial based on {Gerschgorin}'s theorem", journal = NUMAT, volume = "99", number = "1", year = "1991", pages = "349-360" } @book{crt1961, author = "H. Cartan", title = "Th{\'e}orie Elementaire des Fonctions Analytiques d'une ou Plusieurs Variables Complexes", publisher = "Hermann", edition = "4th", year = "1961" } @article{crr1991, author = "R. Carter", title = "{Y-MP} floating point and {Cholesky} factorization", journal = IJHSC, volume = "3", number = "3", year = "1991", pages = "215-222" } @phdthesis{cah1997, author = "L. M. Carvalho", title = "Preconditioned {Schur} complement methods in distributed memory environments", school = "INPT Toulouse", year = "1997", note = "CERFACS report TH/PA/97/41" } @article{cagm2001, author = "L. M. Carvalho and L. Giraud and G. Meurant", title = "Local preconditioners for two-level non-overlapping domain decomposition methods", journal = NLAA, volume = "8", number = "4", year = "2001", pages = "207-227" } @article{cglv2010, author = "L. M. Carvalho and S. Gratton and R. F. Lago and X. Vasseur", title = "Augmentation and truncation for iterative methods", journal = "Anais do CNMAC, Brazil", volume = "3", year = "2010" } @article{cglv2011, author = "L. M. Carvalho and S. Gratton and R. F. Lago and X. Vasseur", title = "A flexible generalized conjugate residual method with inner orthogonalization and deflated restarting", journal = SIMAX, volume = "32", number = "4", year = "2011", pages = "1212-1235" } @article{clo1891, author = "E. Carvallo", title = "Sur les syst{\`e}mes lin{\'{e}}aires, le calcul des symboles diff{\'{e}}rentiels et leur application {\`a} la physique math{\'{e}}matique", journal = MONA, volume = "2", year = "1891", pages = "225-266" } @article{cas1946, author = "G. Cassinis", title = "Risoluzione dei sistemi di equazioni algebriche lineari", journal = "Rend. Sem. Math. Fis. Milano", volume = "17", year = "1946", pages = "62-78" } @article{cwc2008, author = "A. M. Castaldo and R. C. Whaley and A. T. Chronopoulos", title = "Reducing floating point error in dot product using the superblock family of algorithms", journal = SISC, volume = "31", number = "2", year = "2008", pages = "1156-1174" } @misc{caka2023, author = "S. Castillo and J. Kar{\'{a}}tson", title = "Rates of robust superlinear convergence of preconditioned {Krylov} methods for elliptic {FEM} problems", howpublished = "Research Square preprint", year = "2023" } @article{cssz2001, author = "L. Caston and M. Savova and I. Spitkovsky and N. Zobin", title = "On eigenvalues and boundary curvature of the numerical range", journal = LAA, volume = "322", number = "1-3", year ="2001", pages = "129-140" } @article{cgdm2016, author = "N. {Castro-Gonz{\'{a}}lez} and F. M. Dopico and J. M. Molera", title = "Multiplicative perturbation theory of the {Moore-Penrose} inverse and the least squares problem", journal = LAA, volume = "503", year = "2016", pages = "1-25" } @article{ccf2004, author = "L. Catabriga and A. Coutinho and L. P. Franca", title = "Evaluating the {LCD} algorithm for solving linear systems of equations arising from implicit {SUPG} formulation of compressible flows", journal = IJNME, volume = "60", number = "9", year = "2004", pages = "1513-1534" } @article{cvmpc2006, author = "L. Catabriga and A. Valli and B. Melotti and L. Pessoa and A. Coutinho", title = "Performance of {LCD} iterative method in the finite element and finite difference solution of convection-diffusion equations", journal = CNME, volume = "22", number = "6", year = "2006", pages = "643-656" } @inproceedings{ceqr2016, author = "S. Catal{\'{a}}n and P. Ezzatti and E. S. {Quintana-Ort{\'\i}} and A. Rem{\'{o}}n", title = "The impact of panel factorization on the {Gauss-Huard} algorithm for the solution of linear systems on modern architectures", booktitle = "Algorithms and Architectures for Parallel Processing: 16th International Conference", publisher = "Springer", address = "Cham", year = "2016", pages = "405-416" } @article{cat1999, author = "U. V. \c{C}ataly{\"{u}}rek and C. Aykanat", title = "Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication", journal = "IEEE Trans. Parallel Distributed Systems", volume = "10", number = "7", year = "1999", pages = "673-693" } @article{cau1815b, author = "A. L. Cauchy", title = "M{\'{e}}moire sur le nombre de valeurs qu'une fonction peut acqu{\'{e}}rir, lorsqu'on y permute de toutes les mani{\`e}res possibles les quantit{\'{e}}s qu'elle renferme", journal = "Journal de l'{\'{E}}cole Polytechnique", volume = "10", number = "17", year = "1815", pages = "1-27" } @article{cau1815, author = "A. L. Cauchy", title = "M{\'{e}}moire sur les fonctions qui ne peuvent obtenir que deux valeurs {\'{e}}gales et de signes contraires par suite des transpositions op{\'{e}}r{\'{e}}es entre les variables qu'elles renferment", journal = "Journal de l'{\'{E}}cole Polytechnique", volume = "10", number = "17", year = "1815", pages = "29-112" } @book{cau1821, author = "A. L. Cauchy", title = "Cours d'Analyse de l'{\'{E}}cole {R}oyale {P}olytechnique, 1{\`e}re partie {A}nalyse {A}lg{\'{e}}brique", publisher = "Debure fr{\`e}res, libraires du {R}oi", year = "1821" } @incollection{cau1821b, author = "A. L. Cauchy", title = "Sur les formules qui r{\'{e}}sultent de l'emploi du signe $>$ ou $<$, et sur les moyennes entre plusieurs quantit{\'{e}}s", booktitle = "Oeuvres Compl{\`e}tes", volume = "2, tome III", publisher = "Gauthier{-}Villars et Fils", year = "1821", pages = "360-377" } @incollection{cau1826, author = "A. L. Cauchy", title = "Le{\c{c}}ons sur les applications du calcul infinit{\'{e}}simal {\`a} la g{\'{e}}om{\'{e}}trie", booktitle = "Oeuvres Compl{\`e}tes", volume = "2, tome V", publisher = "Gauthier{-}Villars et Fils", year = "1826", pages = "11-528" } @incollection{cau1828, author = "A. L. Cauchy", title = "Sur les centres, les plans principaux et les axes principaux des surfaces du second degr{\'{e}}", booktitle = "Exercices de Math{\'{e}}matiques", publisher = "De Bure Fr{\`e}res", year = "1828" } @incollection{cau1829, author = "A. L. Cauchy", title = "Sur l'{\'{e}}quation {\`a} l'aide de laquelle on d{\'{e}}termine les in{\'{e}}galit{\'{e}}s s{\'{e}}culaires des mouvements des plan{\`e}tes", booktitle = "Oeuvres Compl{\`e}tes", volume = "2, tome IX", publisher = "Gauthier{-}Villars et Fils", year = "1829", pages = "174-95" } @incollection{cau1830, author = "A. L. Cauchy", title = "M{\'{e}}moire sur l'{\'{e}}quation qui a pour racines les moments d'inertie principaux d'un corps solide", booktitle = "Oeuvres Compl{\`e}tes", volume = "1, tome II", publisher = "Gauthier{-}Villars et Fils", year = "1830", pages = "79-81" } @article{cau1837, author ="A. L. Cauchy", title = "M{\'{e}}moire sur l'interpolation", journal = JMPA, volume = "2", year = "1837", pages = "193-205" } @incollection{cau1840, author = "A. L. Cauchy", title = "M{\'{e}}moire sur l'{\'{e}}limination d'une variable entre deux {\'{e}}quations alg{\'{e}}briques", booktitle = "Exercices d'Analyse et de Physique Math{\'{e}}matique, tome I", publisher = "Bachelier", address = "Paris", year = "1840" } @article{cau1841c, author = "A. L. Cauchy", title = "M{\'{e}}moire sur les dilatations, les condensations et les rotations produits par un changement de forme dans un syst{\`e}me de points mat{\'{e}}riels", journal = "Oeuvres S{\'{e}}rie (2)", volume = "12", year = "1841", pages = "343-377" } @incollection{cau1841, author = "A. L. Cauchy", title = "M{\'{e}}moire sur les fonctions altern{\'{e}}es et sur les sommes altern{\'{e}}es", booktitle = "Exercices d'Analyse et de Physique Math{\'{e}}matique, tome II", publisher = "Bachelier", address = "Paris", year = "1841" } @article{cau1841b, author = "A. L. Cauchy", title = "Note sur la formation des fonctions altern{\'{e}}es qui servent {\`a} r{\'{e}}soudre le probl{\`e}me de l'{\'{e}}limination", journal = CRAS, volume = "XII", year = "1841", pages = "414-426" } @article{cau1847, author = "A. L. Cauchy", title = "M{\'{e}}thode g{\'{e}}n{\'{e}}rale pour la r{\'{e}}solution des syst{\`e}mes d'{\'{e}}quations simultan{\'{e}}es", journal = CRAS, volume = "25", year = "1847", pages = "536-538" } @article{cy1958, author = "R. L. Causey", title = "Computing eigenvalues of non-{Hermitian} matrices by methods of {Jacobi} type", journal = SIAMJ, volume = "6", number = "2", year = "1958", pages = "172-181" } @article{cg1961, author = "R. L. Causey and R. T. Gregory", title = "On {Lanczos}' algorithm for tridiagonalizing matrices", journal = SIREV, volume = "3", number = "4", year = "1961", pages = "322-328" } @article{ca1841, author = "A. Cayley", title = "On a theorem in the geometry of position", journal = CMJ, volume = "2", year = "1841", pages = "267-271" } @article{ca1843, author = "A. Cayley", title = "On the theory of determinants", journal = "Trans. Cambridge Philos. Soc.", volume = "8", year = "1843", pages = "1-16" } @article{ca1854, author = "A. Cayley", title = "On the theory of groups as depending on the symbolic equation $\theta^n=1$", journal = PM, volume = "7", year = "1854", pages = "40-47" } @article{ca1855c, author = "A. Cayley", title = "Recherches sur les matrices dont les termes sont des fonctions lin{\'{e}}aires d'une seule ind{\'{e}}termin{\'{e}}e", journal = CRELLE, volume = "50", year = "1855", pages = "313-317" } @article{ca1855a, author = "A. Cayley", title = "Remarques sur la notation des fonctions alg{\'{e}}briques", journal = CRELLE, volume = "50", year = "1855", pages = "282-285" } @article{ca1855b, author = "A. Cayley", title = "Sur la transformation d'une fonction quadratique en elle-m{\^e}me par des substitutions lin{\'{e}}aires", journal = CRELLE, volume = "50", year = "1855", pages = "288-299" } @article{ca1857, author = "A. Cayley", title = "Note sur la m{\'{e}}thode d'{\'{e}}limination de {Bezout}", journal = CRELLE, volume = "53", year = "1857", pages = "366-367" } @article{ca1857b, author = "A. Cayley", title = "On the determination of the value of a certain determinant", journal = "Quart. J. Math.", volume = "2", year = "1857", pages = "163-166" } @article{ca1858, author = "A. Cayley", title = "A memoir on the theory of matrices", journal = PTRSL, volume = "148", year = "1858", pages = "17-37" } @article{ca1866, author = "A. Cayley", title = "A supplementary memoir on the theory of matrices", journal = PTRSL, volume = "156", year = "1866", pages = "25-35" } @article{ca1872, author = "A. Cayley", title = "On the extraction of the square root of a matrix of the third order", journal = PRSE, volume = "7", year = "1872", pages = "675-682" } @article{ca1885b, author = "A. Cayley", title = "On the matrical equation {$qQ-Qq'=0$}", journal = MM, volume = "14", year = "1885", pages = "176-178" } @article{ca1885, author = "A. Cayley", title = "On the quaternion equation {$qQ-Qq'=0$}", journal = MM, volume = "14", year = "1885", pages = "108-112" } @article{ca1889, author = "A. Cayley", title = "Science {W}orthies, {XXV-} {James Joseph Sylvester}", journal = "Nature", volume = "{XXXIX}", number = "1001", year = "1889", pages = "217-219" } @article{ccc1992, author = "J. Cecconi", title = "Lamberto {Cesari}", journal = "Bollettino dell'Unione Matematica Italiana, Sezione A, Serie VII", volume = "6", number = "1", year = "1992", pages = "125-151" } @article{cec1909, author = "F. Cecioni", title = "Sulle equazioni fra matrici {$AX=XB, X^m = A$}", journal = "Atti Acc. Naz. Lincei", volume = "18", number = "5", year = "1909", pages = "566-571" } @article{cec1910, author = "F. Cecioni", title = "Sopra alcune operazioni algebriche sulle matrici", journal = "Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, serie 1", volume = "11", year = "1910", pages = "1-141" } @techreport{ceg2008, author = "A. Cegielski", title = "Methods for finding fixed points of nonexpansive operators in a {Hilbert} space", institution = "Technische Universit{\"a}t Ilmenau, Institut f{\"u}r Mathematik", number = "M 08/20", year = "2008" } @Misc{ceg2010, author = {A. Cegielski}, howpublished = {{\it http://staff.uz.zgora.pl/acegiels/Publications-Kaczmarz-method.pdf}}, title = {A list of publications on the {Kaczmarz} method (up to 2010)}, year = {2010}, } @book{ceg2012, author = "A. Cegielski", title = "Iterative Methods for Fixed Point Problems in {Hilbert} Spaces", note = "Lecture Notes in Mathematics, Vol.~2057", publisher = "Springer-Verlag", address = "Berlin, Heidelberg", year = "2012" } @article{ce1937, author = "L. Cesari", title = "Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive", journal = "La Ricerca Scientifica, Progr. Tecn. Econom. Naz., serie II, anno VIII", volume = "1", number = "11-12", year = "1937", pages = "512-522" } @techreport{ce1937b, author = "L. Cesari", title = "Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive", institution = "Istituto per le applicazioni del calcolo, Consiglio Nazionale delle Richerche", address = "Roma", number = "12", year = "1937" } @article{ce1937c, author = "L. Cesari", title = "Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive", journal = "Rass. Poste, dei Teleg. e dei Telef., anno IX", volume = "4", year = "1937", pages = "285-296" } @article{ce1937d, author = "L. Cesari", title = "Sulla risoluzione dei sistemi di equazioni lineari per approssimazioni successive", journal = "Rendic. Reale Accademia Nazionale dei Lincei, Classe Scienze Fis., Mat., Natur., ser. 6a", volume = "25", year = "1937", pages = "422-428" } @article{ce1946, author = "L. Cesari", title = "Leonida {Tonelli} (1885-1946)", journal = "Bollettino dell'Unione Matematica Italiana, Serie 3", volume = "1", number = "1", year = "1946", pages = "64-67" } @article{cha1989, author = "J. L. Chabert", title = "Gauss et la m{\'{e}}thode des moindres carr{\'{e}}s", journal = RHS, volume = "42", number = "1-2", year = "1989", pages = "5-26" } @book{cha1999, author = "J. L. Chabert", title = "A History of Algorithms. From the Pebble to the Microchip", publisher = "Springer-Verlag", address = "Berlin, Heidelberg", year = "1999" } @book{chac1929, author = "A. B. Chace", title = "The Rhind Mathematical Papyrus, {V}olume {I}", publisher = "Mathematical Association of America", year = "1929" } @book{chac1929b, author = "A. B. Chace and L. Bull and H. P. Manning", title = "The Rhind Mathematical Papyrus, {V}olume {II}", publisher = "Mathematical Association of America", year = "1929" } @techreport{cc1995, author = {F. Chaitin-Chatelin}, title = {Le calcul qualitatif. {C}omment donner un sens {\`a} des r{\'e}sultats faux ?}, year = {1995}, number = {TR/PA/95/10}, institution = {CERFACS}, } @book{ccf1996, author = "F. Chaitin-Chatelin and V. Frayss{\'{e}}", title = "Lectures on Finite Precision Computations", publisher = "SIAM", year = "1996" } @inproceedings{ctp2000, author = "F. Chaitin-Chatelin and E. Traviesas and L. Planti{\'e}", title = "Understanding {Krylov} methods in finite precision", booktitle = "International Conference on Numerical Analysis and Its Applications", publisher = "Springer", address = "Berlin, Heidelberg", year = "2000" } @incollection{cct2005, author = "F. Chaitin-Chatelin and E. Traviesas-Cassan", title = "{PRECISE} and the quality of reliable numerical software", booktitle = "Accuracy and Reliability in Scientific Computing", publisher = "SIAM", year = "2005", pages = "95-108" } @incollection{cct2005b, author = "F. Chaitin-Chatelin and E. Traviesas-Cassan", title = "Qualitative computing", booktitle = "Accuracy and Reliability in Scientific Computing", publisher = "SIAM", year = "2005", pages = "77-92" } @techreport{cbn1986, author = "R. M. Chamberlain", title = "An algorithm for {LU} factorization with partial pivoting on the hypercube", institution = "Chr. Michelsen Institute", number = "CCS 86/11", year = "1986" } @incollection{cbn1987, author = "R. M. Chamberlain", title = "An alternative view of {LU} factorization with partial pivoting on a hypercube multiprocessor", booktitle = "Hypercube Multiprocessors 1987", editor = "M. T. Heath", publisher = "SIAM", year = "1987", pages = "569-575" } @article{ccgsst2020, author = "E. Y. Chan and R. M. Corless and L. {Gonzalez-Vega} and J. R. Sendra and J. Sendra and S. E. Thornton", title = "Upper {Hessenberg} and {Toeplitz} bohemians", journal = LAA, volume = "601", year = "2020", pages = "72-100" } @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{ch1982, author = "T. F. Chan", title = "An improved algorithm for computing the singular value decomposition", journal = TOMS, volume = "8", number = "1", year = "1982", pages = "72-83" } @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" } @article{ch1987b, author = "T. F. Chan", title = "Rank revealing {QR} factorizations", journal = LAA, volume = "88-89", year = "1987", pages = "67-82" } @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" } @misc{chch2000, author = "T. F. Chan and K. Chen", title = "Two-stage preconditioners using wavelet band splitting and sparse approximation", howpublished = "Dpt. of Mathematics, University of California, Los Angeles", year = "2000" } @article{chch2002, author = "T. F. Chan and K. Chen", title = "On two variants of an algebraic wavelet preconditioner", journal = SISC, volume = "24", number = "1", year = "2002", pages = "260-283" } @article{ce1989, author = "T. F. Chan and H. C. 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}, year = {1995}, number = {?}, institution = {Xerox Parc, Palo Alto}, } @book{cgpw1988, author = "T. F. Chan and R. Glowinski and J. P{\'e}riaux 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. P{\'e}riaux and O. B. Widlund Eds.", title = "Third International Symposium on Domain Decomposition Methods for Partial Differential Equations", publisher = "SIAM", year = "1990" } @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" } @techreport{cgo1988, author = {T. F. Chan and D. Goovaerts}, title = {{Schwarz=Schur}: overlapping versus non overlapping domain decomposition}, year = {1988}, number = {CAM 88-21}, institution = {Dept.of Mathematics, UCLA}, } @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}, year = {1990}, number = {CAM 88-16}, institution = {Dept. of Mathematics, UCLA}, } @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" } @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" } @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. P{\'e}riaux 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: {Fourier} analysis and performance on the {Connection} {Machine}", 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" } @article{cmv1997, author = "T. F. Chan and S. D. Margenov and P. S. Vassilevski", title = "Performance of block-{ILU} factorization preconditioners based on block-size reduction for {2D} elasticity systems", journal = SISC, volume = "18", number = "5", year = "1997", pages = "1355-1366" } @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. P{\'e}riaux and O. B. Widlund", publisher = "SIAM", year = "1991", pages = "101-111" } @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" } @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{chm1994, author = "T. F. Chan and T. Mathew", title = "Domain decomposition algorithms", journal = ACTNUM, volume = "3", year = "1994", pages = "61-143" } @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{cpv1991, author = {T. F. Chan and L. {De Pillis} and H. van der Vorst}, institution = {Dpt. of Mathematics, UCLA}, title = {A transpose-free squared {Lanczos} algorithm and application to solving nonsymmetric linear systems}, year = {1991}, number = {91-17 CAM}, } @article{cpv1998, author = "T. F. Chan and L. {De Pillis} and H. van der Vorst", title = "Transpose-free formulations of {Lanczos}-type methods for nonsymmetric linear systems", journal = NUMALGO, volume = "17", number = "1", year = "1998", pages = "51-66" } @techreport{cre1985, author = {T. F. Chan and D. C. Resasco}, title = {A survey of preconditioners for domain decomposition}, year = {1985}, number = {YALEU/DCS/RR-414}, institution = {Dept. of Computer Science, Yale University}, } @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" } @article{cre1987b, author = "T. F. Chan and D. C. Resasco", title = "A domain-decomposed fast {Poisson} solver on a rectangle", journal = SISSC, volume = "8", number = "1", year = "1987", pages = "s14-s26", note = "Errata, SISSC, 8(3), p.~457" } @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" } @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. P{\'e}riaux", 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." } @article{cs1994, author = "T. F. Chan and T. Szeto", title = "A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems", journal = NUMALGO, volume = "7", number = "1", year = "1994", pages = "17-32" } @article{cs1996, author = "T. F. Chan and T. Szeto", title = "Composite step product methods for solving nonsymmetric linear systems", journal = SISC, volume = "17", number = "6", year = "1996", pages = "1491-1508" } @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" } @techreport{ctu1989, author = {T. F. Chan and R. S. Tuminaro}, title = {Analysis of a parallel multigrid algorithm}, year = {1989}, number = {CAM 89-29}, institution = {University of California, Los Angeles}, } @inproceedings{chva2000, author = "T. F. Chan and P. Vanek", title = "Detection of strong coupling in algebraic multigrid solvers", booktitle = "Multigrid Methods VI", editor = " E. Dick and K. Riemslagh and J. Vierendeels", publisher = "Springer", address = "Berlin, Heidelberg", year = "2000", pages = "11-23" } @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" } @techreport{cvdv1994, author = {T. F. Chan and H. A. {van der Vorst}}, title = {Approximate and incomplete factorizations}, year = {1994}, number = {871}, institution = {Dept. of Mathematics, University of Utrecht}, } @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 {Krylov} subspace method for solving nonsymmetric linear systems", journal = AJM, volume = "1", number = "3", year = "1997", pages = "422-434" } @article{chzo1996, author = "T. F. Chan and J. Zou", title = "A convergence theory of multilevel additive {Schwarz} methods on unstructured meshes", journal = NUMALGO, volume = "13", number = "2", year = "1996", pages = "365-398" } @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 = "Dpt. of Computer Science, Yale University", note = "Report 129", 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" } @inproceedings{ces1977, author = "R. Chandra and S. C. Eisenstat and M. H. Schultz", title = "The modified conjugate residual method for partial differential equations", booktitle = "Advances in Computer Methods for Partial Differential Equations {II}", editor = "R. 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Chang", title = "Application of sparse matrix methods in electric power system analysis", booktitle = "Proceedings of the Symposium on Sparse Matrices and their Applications", editor = "R. A. Willoughby", publisher = "IBM, Thomas J. Watson Research Center", year = "1969", pages = "113-122" } @article{chfc2016, author = "F. C. Chang", title = "Matrix inverse as by-product of determinant", journal = "British J. Math. Comput. Sci.", volume = "12", number = "4", year = "2016", pages = "1-21" } @article{cxw2002, author = "{X.-W.} Chang", title = "Some features of {Gaussian} elimination with rook pivoting", journal = BITNM, volume = "42", number = "1", year = "2002", pages = "66-83" } @article{cxw2012, author = "{X.-W.} Chang", title = "On the perturbation of the {Q}-factor of the {QR} factorization", journal = LAA, volume = "19", number = "3", year = "2012", pages ="607-619" } @article{cgp2008, author = "{X.-W.} Chang and G. H. Golub and C. C. Paige", title = "Towards a backward perturbation analysis for data least squares problems", journal = SIMAX, volume = "30", number = "4", year = "2008", pages = "1281-1301" } @article{cp1998, author = "{X.-W.} Chang and C. C. Paige", title = "On the sensitivity of the {LU} factorization", journal = BITNM, volume = "38", number = "3", year ="1998", pages = "486-501" } @article{cp2001, author = {{X.-W.} Chang and C. C. Paige}, journal = NUMAT, title = {Componentwise perturbation analyses for the {QR} factorization}, year = {2001}, number = {2}, pages = {319-345}, volume = {88}, } @article{cp2007, author = "{X.-W.} Chang and C. C. Paige", title = "Euclidean distances and least squares problems for a given set of vectors", journal = ANM, volume = "57", year = "2007", pages = "1240-1244" } @article{cps1996, author = "{X.-W.} Chang and C. C. Paige and G. W. Stewart", title = "New perturbation analyses for the {Cholesky} factorization", journal = IMAJNA, volume = "16", number = "4", year = "1996", pages ="457-484" } @article{cpt2008, author = "{X.-W.} Chang and C. C. Paige and D. Titley-P{\'e}loquin", title = "Characterizing matrices that are consistent with given solutions", journal = SIMAX, volume = "30", number = "4", year = "2008", pages = "1406-1420" } @article{cptp2021, author = "{X.-W.} Chang and C. C. Paige and D. {Titley-Peloquin}", title = "Structure in loss of orthogonality", journal = LAA, volume = "623", year = "2021", pages = "149-167" } @article{chst2010, author = "{X.-W.} Chang and D. 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Higham", title = "Reducing the influence of tiny normwise relative errors on performance profiles", journal = TOMS, volume ="39", number = "4", year = "2013", pages = "1-11" } @inproceedings{dghkpp1992, author = "Q. V. Dinh and R. Glowinski and J. He and V. Kwock and T. W. Pan and J. P{\'e}riaux", 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" } @article{dgp1980b, author = "Q. V. Dinh and R. Glowinski and J. P{\'{e}}riaux", title = "Application of domain decomposition technique to the numerical solution of the {Navier-Stokes} equations", journal = "Numer. Meth. Engng.", volume = "1", year = "1980", pages = "383-404" } @inproceedings{dgp1980, author = "Q. V. Dinh and R. Glowinski and J. P{\'e}riaux", title = "R{\'e}solution num{\'e}rique des {\'e}quations de {Navier-Stokes} par des m{\'e}thodes de d{\'e}composition de domaines", booktitle = "M{\'e}thodes Num{\'e}riques dans les Sciences de l'Ing{\'e}nieur", 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. P{\'e}riaux 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. P{\'e}riaux", publisher = "SIAM", year = "1988", pages = "350-369" } @article{din1900, author = "U. Dini", title = "Eugenio {Beltrami}", journal = "Annali di matematica pura ed applicata", volume = "4", number = "1", year = "1900", pages = "151-152" } @mastersthesis{di2009, author = "R. M. Dinkla", title = "{GMRES}(m) with deflation applied to nonsymmetric systems arising from fluid mechanics problems", school = "Delft University of Technology", address = "Delft, The Netherlands", year = "2009" } @article{dir1926, author = "P. A. M. Dirac", title = "On the theory of quantum mechanics", journal = PRSL, volume = "112", number = "762", year = "1926", pages = "661-677" } @article{drsp2019, author = "D. L. Djuki{\'{c}} and L. Reichel and M. M. Spalevi{\'{c}}", title = "Internality of generalized averaged {Gauss}ian quadrature rules and truncated variants for measures induced by {Chebyshev} polynomials", journal = ANM, volume = "142", year = "2019", pages = "190-205" } @article{drspt2019, author = "D. L. Djuki{\'{c}} and L. Reichel and M. M. Spalevi{\'{c}} and J. D. Tomanovi{\'{c}}", title = "Internality of generalized averaged {Gauss}ian quadrature rules and truncated variants for modified {Chebyshev} measures of the second kind", journal = JCAM, volume = "345", year = "2019", pages = "70-85" } @misc{ddrs2022, author = "D. L. Djuki{\'{c}} and R. M. Djuki{\'{c}} and L. Reichel and M. M. Spalevi{\'{c}}", title = "Internality of generalized averaged Gauss quadrature rules and truncated variants for modified {Chebyshev} measures of the third and fourth kinds", howpublished = "Submitted manuscript", year = "2022" } @misc{dopo2000, author = "F. Dobrian and A. 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Lewis", title = "Sparse extensions to the {Fortran Basic Linear Algebra Subprograms}", journal = TOMS, volume = "17", number = "2", year = "1991", pages = "253-263" } @article{doh2003, author = "C. R. Dohrmann", title = "A preconditioner for substructuring based on constrained energy minimization", journal = SISC, volume = "25", number = "1", year = "2003", pages = "246-258" } @inproceedings{dpw2020, author = "C. R. Dohrmann and K. H. Pierson and O. B. Widlund", title = "On inexact solvers for the coarse problem of {BDDC}", booktitle = "Domain Decomposition Methods in Science and Engineering XXV", editor = "R. Haynes and S. MacLachlan and {X.-C.} Cai and L. Halpern and H. H. Kim and A. Klawonn and O. B. Widlund", publisher = "Springer", year = "2020", pages = "117-124" } @inproceedings{doi1991b, author = "S. Doi", title = "A {Gustafsson}-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{doi1991, author = "S. Doi", title = "On parallelism and convergence of incomplete {LU} factorizations", journal = ANM, volume = "7", number = "5", year = "1991", pages = "417-436" } @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 {Cray}-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" } @article{dow1999, author = "S. Doi and T. Washio", title = "Ordering strategies and related techniques to overcome the trade-off between parallelism and convergence in incomplete factorizations", journal = PARCOMP, volume = "25", number = "13-14", year = "1999", pages = "1995-2014" } @book{djn2015, author = "V. Dolean and P. Jolivet and F. Nataf", title = "An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation", publisher = "SIAM", year = "2015" } @article{dgk2023, author = "V. Dolean and M. J. Gander and A. Kyriakis", title = "Closed form optimized transmission conditions for complex diffusion with many subdomains", journal = SISC, volume = "45", number = "2", year = "2023", pages = "A829-A848" } @article{doti2020, author = "V. Dolej{\v{s}\'{\i}} and P. Tich{\'{y}}", title = "On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates", journal = JSC, volume = "83", number = "1", year = "2020", pages = "1-29" } @article{dosc2010, author = "H. S. Dollar and J. A. Scott", title = "A note on fast approximate minimum degree orderings for matrices with some dense rows", journal = NLAA, volume = "17", year = "2010", pages = "43-55" } @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" } @techreport{ddfgkl2013, author = "S. Donfack and J. J. Dongarra and M. Faverge and M. Gates and J. Kurzak and P. Luszczek", title = "On algorithmic variants of parallel {Gaussian} elimination: {C}omparison of implementations in terms of performance and numerical properties", institution = "INRIA", number = "hal-00867837", year = "2013", note = "Also LAWN 280" } @article{ddfgk2015, author = "S. Donfack and J. J. Dongarra and M. Faverge and M. Gates and J. Kurzak and P. Luszczek and I. Yamazaki", title = "A survey of recent developments in parallel implementations of {Gauss}ian elimination", journal = CPE, volume = "27", number = "5", year = "2015", pages = "1292-1309" } @article{doli1994, author = "S. Dong and K. Liu", title = "Stochastic estimation with $z_2$ noise", journal = "Phys. Lett. B", volume = "328", year = "1994", pages = "130-136" } @techreport{don1980, author = "J. J. Dongarra", title = "{LINPACK} working note 3, {Fortran} {BLAS} timing", institution = "Argonne National Laboratory", number = "ANL-80-24. CM-P00068636", year = "1980" } @misc{don2022, author = "J. J. Dongarra", title = "A not so simple matter of software; {T}he evolution of mathematical software: {S}oftware and algorithms follow the hardware", howpublished = "ACM, to be published", year = "2022" } @techreport{don2023, author = "J. J. Dongarra and al.", title = "Can the {United States} maintain its leadership in high-performance computing?", institution = "Department of Energy, Office of Science", year ="2023" } @techreport{dbms1977, author = "J. J. Dongarra and J. R. Bunch and C. B. Moler and G. W. Stewart", title = "Preliminary {Linpack} user{'}s guide", institution = "Argonne National Laboratory", number = "ANL-AMD-TM-313", note = "Linpack working note \# 9", year = "1977" } @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{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" } @article{ddhh1988b, author = "J. J. Dongarra and J. {Du Croz} and S. Hammarling and R. J. Hanson", title = "Algorithm 656: An extended set of {FORTRAN} basic linear algebra subprograms", journal = TOMS, volume = "14", number ="1", year = "1988", pages = "18-32" } @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{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" } @techreport{ddgh2018, author = "J. J. Dongarra and I. S. Duff and M. Gates and A. Haidar and S. Hammarling and N. J. Higham and J. Hogg and P. Valero Lara and P. Luszczek and M. Zounon and S. D. Relton and S. Tomov and T. Costa and S. Knepper", title = "Batched {BLAS (Basic Linear Algebra Subprograms)} 2018 specification", institution = "Innovative Computing Laboratory, University of Tennessee", number = "ICL-UTK-1170-2018", year = "2018" } @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" } @book{ddsv1998, author = "J. J. Dongarra and I. S. Duff and D. C. Sorensen and H. A. van der Vorst", title = "Numerical linear algebra for high-performance computers", publisher = "SIAM", year = "1998" } @techreport{doei2003, author = "J. J. Dongarra and V. Eijkhout", title = "Finite-choice algorithm optimization in conjugate gradients", institution = "University of Tennessee, Knoxville", number = "UT-CS-03-502", year = "2003" } @article{deli2001, author = "J. J. Dongarra and V. Eijkhout and P. Łuszczek", title = "Recursive approach in sparse matrix {LU} factorization", journal = "Sci. Program.", volume = "9", number = "1", year = "2001", pages = "51-60" } @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" } @inproceedings{dfll2012, author = "J. J. Dongarra and M. Faverge and H. Ltaief and P. Luszczek", title = "Exploiting fine-grain parallelism in recursive {LU} factorization", booktitle = "Applications, Tools and Techniques on the Road to Exascale Computing", publisher = "IOS Press", year = "2012", pages = "429-436" } @article{dfll2014, author = "J. J. Dongarra and M. Faverge and H. Ltaief and P. Luszczek", title = "Achieving numerical accuracy and high performance using recursive tile {LU} factorization with partial pivoting", journal = CCPE, volume = "16", number = "7", year = "2014", pages = "1408-1431" } @article{dghkl2019, author = "J. J. Dongarra and M. Gates and A. Haidar and J.Kurzak and P. Luszczek and al.", title = "{PLASMA}: {P}arallel linear algebra software for multicore using {OpenMP}", journal = TOMS, volume = "45", number = "2", year = "2019", pages = "16:1-16:35" } @techreport{doge2022, author = "J. J. Dongarra and A. Geist", title = "Report on the {Oak Ridge National Laboratory's Frontier} system", institution = "University of Tennessee", number = "ICL-UT-22-05", year = "2022" } @article{dggmm2008, author = "J. J. Dongarra and G. H. Golub and E. Grosse and C. B. Moler and K. Moore", title = "Netlib and {NA-Net}: {B}uilding a scientific computing community", journal = IEAHC, volume = "30", number = "2", year = "2008", pages = "30-41" } @article{dg1985, author = "J. J. Dongarra and E. Grosse", title = "Distribution of mathematical software via electronic mail", journal = "ACM SIGNUM Newsletter", volume = "20", number = "3", year = "1985", pages = "45-47" } @article{dg1987, author = "J. J. Dongarra and E. Grosse", title = "Distribution of mathematical software via electronic mail", journal = CACM, volume = "30", number = "5", year = "1987", pages = "403-407" } @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" } @inproceedings{dhp1997, author = "J. J. Dongarra and S. Hammarling and A. Petitet", title = "Case studies on the development of {ScaLAPACK} and the {NAG} numerical {PVM} library", booktitle = "Quality of Numerical Software", editor = "R. F. Boisvert", publisher = "Springer", address = "Boston, MA", year = "1997", pages = "236-248" } @article{dhl2016, author = "J. J. Dongarra and M. A. Heroux and P. Luszczek", title = "High{-}performance conjugate{-}gradient benchmark: {A} new metric for ranking high{-}performance computing systems", journal = "The International Journal of High Performance Computing Applications", volume = "30", number = "1", year = "2016", pages = "3-10" } @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 {Gigaflop})", journal = SISSC, volume = "7", number = "1", year = "1986", pages = "347-305" } @article{dh1979, author = "J. J. Dongarra and A. R Hinds", title ="Unrolling loops in {Fortran}", journal = SPE, volume = "9", number = "3", year = "1979", pages = "219-226" } @article{dld2003, author = "J. J. Dongarra and P. Luszczek and A. Petitet", title = "The {LINPACK} benchmark: past, present and future", journal = CCPE, volume = "15", number = "9", year = "2003", pages = "803-820" } @article{dms1997, author = "J. J. Dongarra and H. W. Meuer and E. Strohmaier", title = "{TOP500} supercomputer sites", journal = "Supercomputer", volume = "13", year = "1997", pages = "89-111" } @misc{dmss2000, author = "J. J. Dongarra and H. W. Meuer and H. D. Simon and E. Strohmaier", title = "High performance computing today", howpublished = "Lawrence Berkeley National Laboratory", year = "2000" } @techreport{dm1980, author = "J. J. Dongarra and C. B. Moler", title = "Implementation guide for {Linpack}", institution = "Argonne National Laboratory", number = "ANL-80-105", note = "Linpack working note \# 13", year = "1980" } @inproceedings{dm1984, author = "J. J. Dongarra and C. B. Moler", title = "Eispack: A package for solving matrix eigenvalue problems", booktitle = "Sources and Development of Mathematical Software", editor = "W. R. Cowell", publisher = "Prentice-Hall", address = "Englewood Cliffs, NJ", year = "1984", pages = "68-87" } @misc{dora2000, author = "J. J. Dongarra and P. Raghavan", title = "A new recursive implementation of sparse {Cholesky} factorization", howpublished = "Proceedings of the 16th IMACS World Congress on Scientific Computing, Applications, Mathematics, and Simulation", year = "2000" } @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{dso1987, author = "J. J. Dongarra and D. C. Sorensen", title = "A fully parallel algorithm for the symmetric eigenvalue problem", journal = SISSC, volume = "8", year = "1987", pages = "139-154" } @techreport{ds1982, author = "J. J. Dongarra and G. W. Stewart", title = "Linpack - {A} package for solving linear systems", note = "Linpack working note 15", institution = "Argonne National Laboratory", number = "ANL-82-30", year = "1982" } @article{dtlkgyaha2017, author = "J. Dongarra and S. Tomov and P. Luszczek and J. Kurzak and M. Gates and I. Yamazaki and H. Anzt and A. Haidar and A. Abdelfattah", title = "With extreme computing the rules have changed", journal = CSE, volume = "19", number = "3", note = "IEEE", year = "2017", pages = "52-62" } @article{dw1996, author = "J. J. Dongarra and D. Walker", title = "{MPI}: {A} standard message passing interface", journal = "Supercomputer", volume = "12", number = "1", year = "1996", pages = "56-68" } @techreport{dow1993, author = {J. J. Dongarra and D. W. Walker}, title = {The design of linear algebra libraries for high performance computers}, year = {1993}, number = {ORNL/TM-12404}, institution = {Oak Ridge National Lab.}, } @article{dw2000, author = "J. J. Dongarra and J. Wa\'{s}niewski", title = "LAPACK95 {-} high performance linear algebra package", journal = "Math. Model. Anal.", volume = "5", number = "1", year = "2000", pages = "44-54" } @article{dly1971, author = "J. D. P. Donnelly", title = "Periodic chaotic relaxation", journal = LAA, volume = "4", number = "2", year = "1971", pages = "117-128" } @article{dgh1957, author = "W. F. Donoghue", title = "On the numerical range of a bounded operator", journal = "Michigan Math. J.", volume = "4", number = "3", year = "1957", pages = "261-263" } @incollection{doo1881, author = "M. H. Doolittle", booktitle = "Report of the Superintendant of the U.S. Coast and Geodetic Survey showing the progress of the work during fiscal year ending June 1878", title = "Explanations and illustrations of method employed in the office in solution of normal equations and the adjustment of a triangulation", publisher = "Government Publishing Office", address = "Washington", year = "1881", pages = "115-120" } @article{domo2005, author = "F. M. Dopico and J. M. Molera", title = "Perturbation theory for factorizations of {LU} type through series expansions", journal = SIMAX, volume = "27", number = "2", year = "2005", pages = "561-581" } @article{dkmo2009, author = "F. M. Dopico and P. Koev and J. M. Molera", title = "Implicit standard {Jacobi} gives high relative accuracy", journal = NUMAT, volume = "113", number = "4", year = "2009", pages = "519-553" } @article{douh2016, author = "F. M. Dopico and F. Uhlig", title = "Computing matrix symmetrizers, part 2: {N}ew methods using eigendata and linear means; a comparison", journal = LAA, volume = "504", year = "2016", pages = "590-622" } @article{dosc1994, author = "P. D{\"{o}}rfler and G. Schmeisser", title = "Construction of unitary and normal companion matrices", journal = LAA, volume = "202", year = "1994", pages = "193-220" } @misc{dor1990, author = "J. L. Dorier", title = "Analyse historique de l'{\'{e}}mergence des concepts {\'{e}}l{\'{e}}mentaires d'alg{\`e}bre lin{\'{e}}aire", howpublished = "hal-02138152", year = "1990" } @article{dor1993, author = "J. L. Dorier", title = "Emergence du concept de rang dans l'{\'{e}}tude des syst{\`e}mes d'{\'{e}}quations lin{\'{e}}aires", journal = "Cahiers du S{\'{e}}minaire d'Histoire des Math{\'{e}}matiques 2{\'{e}}me s{\'{e}}rie", volume = "3", year = "1993", pages = "159-190" } @article{dor1995, author = "J. L. Dorier", title = "A general outline of the genesis of vector space theory", journal = HM, volume = "22", number = "3", year = "1995", pages = "227-261" } @article{drr1970, author = "F. W. Dorr", title = "The direct solution of the discrete {Poisson} 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 {Poisson} equation in {O}($n^2$) operations", journal = SIREV, volume = "17", number = "3", year = "1975", pages = "412-415" } @article{do1988, author = "Z. 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Wu", title = "Numerical ranges of companion matrices", journal = LAA, volume = "421", number = "2", year = "2007", pages = "202-218" } @phdthesis{gau2014, author = "A. Gaul", title = "Recycling {Krylov} subspace methods for sequences of linear systems", school = "Technical University Berlin", year = "2014" } @article{ggln2013, author = "A. Gaul and M. H. Gutknecht and J. Liesen and R. Nabben", title = "A framework for deflated and augmented {Krylov} subspace methods", journal = SIMAX, volume = "34", number = "2", year = "2013", pages = "495-518" } @article{gau1927, author = "J. A. Gaunt", title = "The deferred approach to the limit. {Part II}: {I}nterpenetrating lattices", journal = PTRSL, volume = "226", year = "1927", pages = "350-361" } @book{gauss1801, author = "C. F. Gauss", title = "Disquisitiones Arithmeticae", publisher = "Gerhard Fleischer", address = "Leipzig", year = "1801" } @book{gauss1809b, author = "C. F. 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Golub", series = "Studies in Mathematics", volume = "24", publisher = "Mathematical Association of America", address = "Washington, D.C.", year = "1984", pages = "140-177" } @inproceedings{gaut1984, author = "W. Gautschi", title = "Questions of numerical condition related to polynomials", booktitle = "Studies in Numerical Analysis", editor = "G. H. Golub", series = "Studies in Mathematics", publisher= "MAA", volume = "24", year = "1985", pages = "140-177" } @article{gaut1985, author = "W. Gautschi", title = "Orthogonal polynomials - constructive theory and applications", journal = JCAM, volume = "12-13", year = "1985", pages = "61-76" } @inproceedings{gaut1990, author = "W. Gautschi", title = "How (un)stable are {Vandermonde} systems?", booktitle = "Asymptotic and Computational Analysis", editor = "R. Wong", series = "Lectures notes in pure and applied mathematics", volume = "124", publisher = "Marcel Dekker", year = "1990", pages = "193-210" } @article{gaut1997, author = "W. 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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 {Cholesky} factorization on a shared memory multiprocessor", journal = LAA, volume = "77", year = "1986", pages = "165-187" } @article{ghln1986, author = "J. A. George and M. T. Heath and J. W. H. Liu and E. G. Ng", title = "Solution of sparse positive definite systems on a shared-memory multiprocessor", journal = IJPP, volume = "15", number = "4", year = "1986", pages = "309-325" } @article{ghln1988, author = "J. A. George and M. T. Heath and J. W. H. Liu and E. G. Ng", title = "Sparse {Cholesky} factorization on a local memory multiprocessor", journal = SISSC, volume = "9", number = "2", year = "1988", pages = "327-340" } @article{ghln1989, author = "J. A. George and M. T. Heath and J. W. H. Liu and E. G. Ng", title = "Solution of sparse positive definite systems on a hypercube", journal = JCAM, volume = "27", year = "1989", pages = "129-156" } @article{ghnl1987, author = "J. A. George and M. T. Heath and E. G. Ng and J. W. H. Liu", title = "Symbolic {Cholesky} factorization on a local memory multiprocessor", journal = PARCOMP, volume = "5", number = "1-2", year = "1987", pages = "85-96" } @article{gi1996, author = "J. A. George and Kh. 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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{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" } @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" } @book{gl1981, author = "J. A. George and J. W. H. 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Murray and J. {von Neumann}", title = "The {Jacobi} method for real symmetric matrices", journal = JACM, volume = "6", number = "1", year = "1959", pages = "59-96" } @article{gvn1951, author = "H. H. Goldstine and J. {von Neumann}", title = "Numerical inverting of matrices of high order. {II}", journal = PAMS, volume = "2", number = "2", year = "1951", pages = "188-202" } @inproceedings{gvn1963, author = "H. H. Goldstine and J. {von Neumann}", title = "On the principles of large scale computing machines", booktitle = "John von Neumann Collected Works, Vol. 5", editor = "A. H. Taub", publisher = "Macmillan", address = "New York", year = "1963", pages = "1-33" } @misc{gvn1948, author = "H. H. Goldstine and J. {von Neumann}", title = "Planning and coding of problems for an electronic computing instrument, {Parts I, II, III}", howpublished = "Institute for Advanced Study, Princeton, New Jersey", year = "1947-1948" } @article{gnv1995, author = "L. Golinskii and P. Nevai and W. {Van Assche}", title = "Perturbation of orthogonal polynomials on an arc of the unit circle", journal = JAT, volume = "83", number = "3", year = "1995", pages = "392-422" } @article{goma2014, author = "E. {Golpar-Raboky} and N. {Mahdavi-Amiri}", title = "{WZ} factorization via {Abaffy-Broyden-Spedicato} algorithms", journal = "Bull. Iranian Mth. Soc.", volume = "40", number = "2", year = "2014", pages = "399-411" } @article{goma2014b, author = "E. {Golpar-Raboky} and N. {Mahdavi-Amiri}", title = "A new interpretation of the integer and real {WZ} factorization using block scaled {ABS} algorithms", journal = "Stat. Optim. Inf. Comput.", volume = "2", year = "2014", pages = "243-256" } @phdthesis{go1959, author = "G. H. Golub", title = "The use of {Chebyshev} matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxation", school = "Dept. of Computer Science, University of Illinois at Urbana-Champaign", year = "1959" } @article{go1962b, author = "G. H. Golub", title = "Bounds for eigenvalues of tridiagonal symmetric matrices computed by the {LR} method", journal = MATCOMP, volume = "16", year = "1962", pages = "438-445" } @article{go1962, author = "G. H. Golub", title = "Bounds for the round-off errors in the {Richardson} second order method", journal = BITNM, volume = "2", number = "4", year = "1962", pages = "212-223" } @article{go1965, author = "G. H. Golub", title = "Numerical methods for solving linear least squares problems", journal = NUMAT, volume = "7", year = "1965", pages = "206-216" } @article{go1968, author = "G. H. Golub", title = "Least squares, singular values and matrix approximations", journal = "Aplikace Matematiky", volume = "13", number = "1", year = "1968", pages = "44-51" } @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" } @inproceedings{go1995, author = "G. H. Golub", title = "Matrix computation and the theory of moments", booktitle = "Proceedings of the International Congress of Mathematicians, Z{\"u}rich, Switzerland 1994", editor = "S. D. Chatterji", publisher = "Birkh{\"a}user", address = "Basel", year = "1995", pages = "1440-1448" } @article{gof1992, author = "G. H. Golub and B. Fischer", title = "How to generate unknown orthogonal polynomials out of known orthogonal polynomials", journal = JCAM, volume = "43", year = "1992", pages = "99-115" } @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{ghol1999, author = "G. H. Golub and P. C. Hansen and D. P. {O'Leary}", title = "Tikhonov regularization and total least squares", journal = SIMAX, volume = "21", number = "1", year = "1999", pages = "185-194" } @article{ghw1979, author = "G. H. Golub and M. Heath and G. Wahba", title = "Generalized cross-validation as a method to choosing a good ridge parameter", journal = TEC, volume = "21", number = "2", year = "1979", pages = "215-223" } @article{ghs1987, author = "G. H. Golub and A. Hoffman and G. W. Stewart", title = "A generalization of the {Eckart-Young-Mirsky} matrix approximation theorem", journal = LAA, volume = "88", year = "1987", pages = "317-327" } @article{gk1965, author = "G. H. Golub and W. Kahan", title = "Calculating the singular values and pseudo-inverse of a matrix", journal = SINUM, volume = "2", number = "2", year = "1965", pages = "205-224" } @article{gok1986, author = "G. H. Golub and R. Kannan", title = "Convergence of a two-stage {Richardson} 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 {Gauss} quadratures with multiple free and fixed knots", journal = NUMAT, volume = "41", year = "1983", pages = "147-163" } @article{goke1989, author = "G. H. Golub and M. D. Kent", title = "Estimates of eigenvalues for iterative methods", journal = MATCOMP, volume = "53", number = "188", year = "1989", pages = "619-626" } @techreport{gks1976, author = "G. H. Golub and V. Klema and G. W. Stewart", title = "Rank degeneracy and least squares problems", institution = "Stanford University, Dept. of Computer Science", number = "STAN-CS-76-559", year = "1976" } @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" } @article{gvl1980, author = "G. H. Golub and C. F. {Van Loan}", title = "An analysis of the total least squares problem", journal = SINUM, volume = "17", number = "6", year = "1980", pages = "883-893" } @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" } @book{gvl2013, author = "G. H. Golub and C. F. {Van Loan}", title = "Matrix {C}omputations", edition = "4th", publisher = "Johns Hopkins University Press", address = "Baltimore", year = "2013" } @inproceedings{golu1976, author = "G. H. Golub and F. T. Luk", title = "Singular value decomposition: {A}pplications and computations", booktitle = "Transactions of the Twenty-Second Conference of Army Mathematicians", publisher = "US Army Research Office", year = "1976", pages = "577-605" } @article{gvm1991, author = "G. H. Golub and U. {von Matt}", title = "Quadratically constrained least squares and quadratic problems", journal = NUMAT, volume = "59", year = "1991", pages = "561-580" } @inproceedings{gvm1997, author = "G. H. Golub and U. {von Matt}", title = "Generalized cross-validation for large scale problems", booktitle = "Recent Advances in Total Least Squares Techniques and Errors-in-variable Modelling", editor = "S. {van Huffel}", publisher = "SIAM", address = "Philadelphia", year = "1997", pages = "139-148" } @inproceedings{gvm1997b, author = "G. H. Golub and U. {von Matt}", title = "Tikhonov regularization for large scale problems", booktitle = "Scientific Computing", editor = "G. H. Golub and S. H. Lui and F. Luk and R. Plemmons", publisher = "Springer", address = "Berlin", year = "1997", pages = "3-26" } @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" } @article{gomo2001, author = "G. H. Golub and H. Melb\o", title = "A stochastic approach to error estimates for iterative linear solvers, part 1", journal = BITNM, volume = "41", number = "5", year = "2001", pages = "977-985" } @techreport{gomo2001b, author = {G. H. Golub and H. Melb\o}, title = {A stochastic approach to error estimates for iterative linear solvers, part 2}, year = {2001}, number = {SCCM-01-05}, institution = {Stanford University, Computer Science Dept.}, } @book{gom1983, author = "G. H. Golub and G. Meurant", title = "R{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes Lin{\'e}aires", 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 = BITNM, volume = "37", number = "3", year = "1997", pages = "687-705" } @book{gme2010, author = "G. H. Golub and G. Meurant", title = "Matrices, Moments and Quadrature with Applications", publisher = "Princeton University Press", year = "2010" } @article{gom1987, author = "G. H. Golub and C. B. Moler", title = "Dedication to {J}. {H}. {Wilkinson}", journal = LAA, volume = "88/89", number = "1-3", year = "1987", pages = "1-3" } @article{gnv1979, author = "G. H. Golub and S. Nash and C. Van Loan", title = "A {Hessenberg}-{Schur} method for the problem {$AX+XB=C$}", journal = ITAC, volume = "24", number = "6", year = "1979", pages = "909-913" } @article{gol1989, author = "G. H. Golub and D. P. {O{'}Leary}", title = "Some history of the conjugate gradient and {Lanczos} 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 {Richardson} iterative procedure for solving systems of linear equations}, year = {1981}, number = {NA-81-17}, institution = {Computer Science Dept., Stanford University}, } @article{gov1988, author = "G. H. Golub and M. L. Overton", title = "The convergence of inexact {Chebyshev} and {Richardson} iterative methods for solving linear systems", journal = NUMAT, volume = "53", number = "5", year = "1988", pages = "571-593" } @inproceedings{godp1990, author = {G. H. Golub and J. E. {de Pillis}}, booktitle = {Iterative Methods for Large Linear Systems}, title = {Toward an effective two-parameter {SOR} method}, year = {1990}, editor = {D. R. Kincaid and L. J. Hayes}, pages = {107-119}, publisher = {Academic Press}, } @article{gr1970, author = "G. H. Golub and C. Reinsch", title = "Singular value decomposition and least squares solutions", journal = NUMAT, volume = "14", year = "1970", pages = "403-420" } @article{grt2007, author = "G. H. Golub and D. Ruiz and A. Touhami", title = "A hybrid approach combining {Chebyshev} filter and conjugate gradient for solving linear systems with multiple right-hand sides", journal = SIMAX, volume = "29", number = "3", year = "2007", pages ="774-795" } @article{gsvd2000, author = "G. H. Golub and K. S{{\o}}lna and P. {Van Dooren}", title = "Computing the {SVD} of a general matrix product/quotient", journal = SIMAX, volume = "22", number = "1", year = "2000", pages = "1-19" } @article{gsw2008, author = "G. H. Golub and M. Stoll and A. Wathen", title = "Approximation of the scattering amplitude and linear systems", journal = ETNA, volume = "31", year = "2008", pages = "178-203" } @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" } @article{gu2009, author = "G. H. Golub and F. Uhlig", title = "The {QR} algorithm: 50 years later its genesis by {J}ohn {Francis} and {V}era {Kublanovskaya} and subsequent developments", journal = IMAJNA, volume = "29", number = "3", year = "2009", pages = "467-485" } @inproceedings{gu1977, author = "G. H. Golub and R. Underwood", title = "The block {Lanczos} 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" } @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" } @incollection{gvdv1997b, author = "G. H. Golub and H. A. {van der Vorst}", title = "150 years old and still alive: {E}igenproblems", booktitle = "The State of the Art in Numerical Analysis", editor = "I. S. Duff and G. A. Watson", publisher = "Oxford University Press", year = "1997", pages = "93-119" } @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{gvdv1997c, author = "G. H. Golub and H. A. {van der Vorst}", title = "Eigenvalue computation in the 20th century", journal = JCAM, volume = "123", number = "1-2", year = "2000", pages = "35-65" } @inproceedings{gvdv2001, 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 = "2001", pages = "63-92" } @techreport{gw1967, author = "G. H. Golub and J. H. Welsch", title = "Calculation of {Gauss} quadrature rules", institution = "Stanford University, Computer Science Dept.", number = "CS 81", year = "1967" } @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{gwi1976, author = "G. H. Golub and J. H. Wilkinson", title = "Ill-conditioned eigensystems and the computation of the {Jordan} canonical form", journal = SIREV, volume = "18", number = "4", year = "1976", pages = "578-619" } @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" } @article{gye2000, author = "G. H. Golub and Q. Ye", title = "Inexact inverse iteration for generalized eigenvalue problems", journal = BIT, volume = "40", number = "4", year = "2000", pages = "671-684" } @article{gyzh1994, author = "G. H. Golub and H. Zha", title = "Perturbation analysis of the canonical correlations of matrix pairs", journal = LAA, volume = "210", year = "1994", pages = "3-28" } @article{grt2008, author = "M. Gomes-Ruggiero and V. Rocha Lopes and J. Toledo-Benavides", title = "A safeguard approach to detect stagnation of {GMRES}(m) with applications in {Newton}-{Krylov} methods", journal = COAM, volume = "27", number = "2", year = "2008", pages = "175-199" } @phdthesis{gnn2009, author = "P. Gonnet", title = "Adaptive quadrature re-revisited", school = "ETH Z{\"{u}}rich", year = "2009" } @article{gptr2011, author = "P. Gonnet and R. Pach{\'{o}}n and L. N. Trefethen", title = "Robust rational interpolation and least-squares", journal = ETNA, volume = "38", year = "2011", pages = "146-167" } @article{ggtr2013, author = "P. Gonnet and S. G{\"{u}}ttel and L. N. Trefethen", title = "Robust {Pad{\'e}} approximation via {SVD}", journal = SIREV, volume = "55", number = "1", year = "2013", pages = "101-117" } @article{gosc2016, author = "C. C. Gonzaga and R. M. Schneider", title = "On the steepest descent algorithm for quadratic functions", journal = "Comput. Optim. Appl.", volume = "63", number = "2", year = "2016", pages = "523-542" } @article{gbc2018, author = "S. L. Gonzaga de Oliveira and J. A. B. Bernardes and G. O. Chagas", title = "An evaluation of reordering algorithms to reduce the computational cost of the incomplete {Cholesky}-conjugate gradient method", journal = COAM, volume = "37", number = "3", year = "2018", pages = "2965-3004" } @article{gcp2000, author = "P. Gonz{\'{a}}lez and J. C. Cabaleiro and T. F. Pena", title = "On parallel solvers for sparse triangular systems", journal = "J. Syst. Archit.", volume = "46", number = "8", year = "2000", pages = "675-685" } @phdthesis{goz1986, author = "R. Gonzalez", title = "Domain decomposition for two dimensional elliptic operators on vector and parallel machines", school = "Rice University", year = "1986" } @article{gmtt2011, author = "J. {Gonz{\'{a}}lez-Dom{\'\i}nguez} and M. J. Mart{\'\i}n and G. L. Taboada and J. Tourino", title = "Dense triangular solvers on multicore clusters using {UPC}", journal = PCS, volume = "4", year = "2011", pages = "231-240" } @article{grt2012, author = "E. {Gonz{\'{a}}lez-Guti{\'e}rrez} and L. {Hern{\'{a}}ndez Rebollar} and M. I. Todorov", title = "Relaxation methods for solving linear inequality systems: converging results", journal = "TOP", volume = "20", year ="2012", pages ="426-436" } @article{goo1958, author = "I. J. Good", title = "The interaction algorithm and practical {Fourier} 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 = ITCO, volume = "20", year = "1971", pages = "310-317" } @article{gmrs1995, author = "T. N. T. Goodman and C. A. Micchelli and G. Rodriguez and S. Seatzu", title = "On the {Cholesky} factorization of the {Gram} matrix of locally supported functions", journal = BITNM, volume = "35", number = "2", year = "1995", pages = "233-257" } @article{goo2020, author = "J. R. Goodstein", title = "Olga {Taussky-Todd}", journal = NAMS, volume = "67", number = "3", year = "2020", pages = "345-353" } @article{gor1999, author = "S. Goossens and D. Roose", title = "Ritz and harmonic {Ritz} values and the convergence of {FOM} and {GMRES}", journal = NLAA, volume = "6", number = "4", year = "1999", pages = "281-293" } @phdthesis{gvs1990, author = "D. Goovaerts", title = "Domain decomposition for elliptic partial differential equations", school = "Katholieke Universiteit Leuven", year = "1990" } @article{gotr2019, author = "A. Gopal and L. N. Trefethen", title = "New {Laplace} and {Helmholtz} solvers", journal = PNAS, volume = "116", number = "21", year = "2019", pages = "10223-10225" } @article{gotr2019b, author = "A. Gopal and L. N. Trefethen", title = "Representation of conformal maps by rational functions", journal = NUMAT, volume = "142", number = "2", year = "2019", pages = "359-382" } @article{gor2005, author = "D. Gordon", title = "Parallel {ART} for image reconstruction in {CT} using processor arrays", journal = "Int. J. Parallel Emergent Distrib. Syst.", volume = "21", year = "2005", pages = "365-380" } @article{gor2018, author = "D. Gordon", title = "The {Cimmino-Kaczmarz} equivalence and related results", journal = "Appl. Anal. Optim.", volume = "2", year = "2018", pages = "253-270" } @article{gbh1970, author = "R. Gordon and R. Bender and G. T. Herman", title = "Algebraic reconstruction techniques {(ART)} for three-dimensional electron microscopy and x-ray photography", journal = "J. Theor. Biol.", volume = "29", year = "1970", pages = "471-481" } @article{gcgmrl2019, author = "C. Gorman and G. Ch{\'{a}}vez and P. Ghysels and T. Mary and F. H. Rouet and X. S. Li", title = "Robust and accurate stopping criteria for adaptive randomized sampling in matrix-free hierarchically semiseparable construction", journal = SISC, volume = "41", number = "5", year = "2019", pages = "S61-S85" } @book{gos1577, author = "G. Gosselin", title = "De Arte Magna, seu de Occulta Parte Numerorum quae et {A}lgebra et {A}lmucabala Vulgo Dicitur", publisher = "Gilles Bets", address = "Paris", year = "1577" } @article{goto2008, author = "C. Gotsman and S. Toledo", title = "On the computation of null spaces of sparse rectangular matrices", journal = SIMAX, volume = "30", number = "2", year = "2008", pages = "445-463" } @incollection{gou1996, author = "D. Gough", title = "The success story of the transfer and development of methods from geophysics to helioseismology", booktitle = "Inverse Methods", editor = "B. H. Jacobsen and K. Mosegaard and P. Sibani", publisher = "Springer", address = "Berlin, Heidelberg", year = "1996", pages = "1-31" } @article{gou1991, author = "N. Gould", title = "On growth in {Gauss}ian elimination with complete pivoting", journal =SIMAX, volume = "12", number = "2", year = "1991", pages = "354-361" } @techreport{gsc1995, author = {N. I. Gould and J. A. Scott}, institution = {Rutherford Appleton Laboratory}, title = {On approximate inverse preconditioners}, year = {1995}, address = {UK}, number = {RAL-TR-95-026}, } @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{gsh2007, author = "N. I. Gould and J. A. Scott and Y. Hu", title = "A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations", journal = TOMS, volume = "33", number = "2", year = "2007", pages = "1-32" } @article{goou1968, author = "A. R. Gourlay", title = "The acceleration of the {Peaceman-Rachford} method by {Chebyshev} polynomials", journal = COMPJ, volume = "10", year = "1968", pages = "378-382" } @article{goou1970, author = "A. R. Gourlay", title = "On {Chebychev} acceleration procedures for alternating direction iterative methods", journal = JIMA, volume = "6", year = "1970", pages = "1-11" } @article{gor2015, author = "R. Gower and P. Richt{\'a}rik", title = "Randomized iterative methods for linear systems", journal = SIMAX, volume = "36", number = "4", year = "2015", pages = "1660-1690" } @incollection{gow2011, author = "T. Gowers", title = "Is {M}athematics discoverd or invented?", booktitle ="Meaning in Mathematics", editor = "J. Polkinghorne", publisher = "Oxford University Press", year = "2011", pages = "3-12" } @misc{gaa2012, author = "M. M. Gra{\c{c}}a", title = "Quadrature as a least-squares and minimax problem", howpublished = "ArXiv preprint arXiv:1206.0281", year = "2012" } @article{gra1972, author = "W. B. Gragg", title = "The {Pad{\'e}} table and its relation to certain algorithms of numerical analysis", journal = SIREV, volume = "14", number = "1", year = "1972", pages ="1-62" } @article{gra1974, author = "W. B. Gragg", title = "Matrix interpretations and applications of the continued fraction algorithm", journal = RMJM, volume = "4", number = "2", year = "1974", pages = "213-225" } @article{gra1986, author = "W. B. Gragg", title = "The {QR} algorithm for unitary {Hessenberg} matrices", journal = JCAM, volume = "16", year = "1986", pages = "1-8" } @article{gra1993, author = "W. B. Gragg", title = "Positive definite {Toeplitz} matrices, the {Arnoldi} process for isometric operators, and {Gauss}ian quadrature on the unit circle", journal = JCAM, volume = "46", year = "1993", pages = "183-198" } @article{grh1984, author = "W. B. Gragg and W. J. Harrod", title = "The numerically stable reconstruction of {Jacobi} matrices from spectral data", journal = NUMAT, volume = "44", number = "3", year = "1984", pages = "317-335" } @article{gral1983, author = "W. B. Gragg and A. Lindquist", title = "On the partial realization problem", journal = LAA, volume = "50", year = "1983", pages = "277-319" } @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-{Hermitian} matrices", journal = LAA, volume = "88", year = "1987", pages = "349-371" } @article{grar1990, author = "W. B. Gragg and L. Reichel", title = "A divide and conquer method for unitary and orthogonal eigenproblems", journal = NUMAT, volume = "57", number = "1", year = "1990", pages = "695-718" } @article{grar1976, author = "W. B. Gragg and G. W. 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Forsythe}", journal = CACM, volume = "15", number = "8", year = "1972", pages = "719-720" } @article{hmsc1987, author = "D. Hershkowitz and V. Mehrmann and H. Schneider", title = "Eigenvalue interlacing for certain classes of matrices with real principal minors", journal = LAA, volume = "88", year = "1987", pages = "373-403" } @article{he1949, author = "M. Herzberger", title = "The normal equations of the method of least squares and their solution", journal = QAM, volume = "7", year = "1949", pages = "217-223" } @techreport{hes1940, author = "K. Hessenberg", title = "Behandlung linearer eigenwertaufgaben mit hilfe der {Hamilton}-{Cayleyschen} gleichung", number = "1) Bericht der Reihe Numerische Verfahren", institution = "Institut f{\"u}r Praktische Mathematik, Technische Hochschule Darmstadt", year = "1940" } @phdthesis{hes1940b, author = "K. Hessenberg", title = "Die berechnung der eigenwerte und eigenl{\"{o}}sungen linearer gleichungesysteme", school = "Technische Hochschule Darmstadt", address = "Germany", year = "1940" } @inproceedings{hes2011, author = "D. Hestenes", title = "Grassmann{'}s legacy", booktitle = "From Past to Future: {Gra{\ss}mann}{'}s Work in Context", editor = "H. J. Petsche and A. Lewis and J. Liesen and S. Russ", publisher = "Springer", address = "Basel", year = "2011" } @techreport{he1951, author = {M. R. Hestenes}, title = {Iterative methods for solving linear equations}, year = {1951}, note = {Reprinted in J. of Optimization Theory and Applications, v.~11, (1973), pp.~323-334}, number = {52-9}, institution = {NAML, National Bureau of Standards}, } @techreport{hes1954, author = {M. R. Hestenes}, title = {The conjugate gradient method for solving linear systems}, year = {1954}, number = {INA 54-11}, institution = {National Bureau of Standards}, } @article{hes1955, author = "M. R. Hestenes", title = "Iterative computational methods", journal = CPAM, volume = "8", number = "1", year = "1955", pages = "85-95" } @inproceedings{hes1956, author = "M. R. Hestenes", title = "The conjugate gradient method for solving linear systems", booktitle = "Numerical Analysis, Proc. Symp. Appl. Math VI,", editor = "J. H. Curtiss", publisher = "American Mathematical Society", year = "1956", pages = "83-102" } @article{hes1958, author = "M. R. Hestenes", title = "Inversion of matrices by biorthogonalization and related results", journal = SIAMJ, volume = "6", number = "1", year = "1958", pages = "51-90" } @article{hes1973, author = "M. R. Hestenes", title = "Iterative methods for solving linear equations", journal = JOTA, volume = "11", number = "4", year = "1973", pages = "323-334" } @book{hes1980, author = "M. R. Hestenes", title = "Conjugate Direction Methods in Optimization", publisher = "Springer", year = "1980" } @inproceedings{hes1990, author = "M. R. Hestenes", title = "Conjugacy and gradients", booktitle = "A History of Scientific Computing", editor = "S.G. Nash", publisher = "ACM Press", year = "1990", pages = "167-179" } @article{hk1951, author = "M. R. Hestenes and W. Karush", title = "A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix", journal = JNBS, volume = "47", number = "1", year = "1951", pages = "45-61" } @article{hems1940, author = "M. R. Hestenes and E. J. McShane", title = "A theorem on quadratic forms and its application in the calculus of variations", journal = TAMS, volume = "47", number = "3", year = "1940", pages = "501-512" } @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" } @techreport{ht1991, author = "M. R. Hestenes and J. Todd", title = "{NBS-INA}. the {Institute for Numerical Analysis}, {UCLA} 1947-1954", institution = "NIST", number = "Special Publication 730", year = "1991" } @article{htv1998, author = "J. S. Hesthaven", title = "From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex", journal = SINUM, volume = "35", number = "2", year = "1998", pages = "655-676" } @article{het2015, author = "C. Hettle", title = "The symbolic and mathematical influence of {Diophantus}' {Arithmetica}", journal = "Journal of Humanistic Mathematics", volume = "5", number = "1", year = "2015", pages = "139-166" } @article{hmo1987, author = "K. J. Heuvers and D. Moak", title = "Matrix solutions of the functional equation of the gamma function", journal = "Aequationes Mathematicae", volume = "33", number = "1", year = "1987", pages = "1-17" } @article{hey2001, author = "M. Heyouni", title = "The global {Hessenberg} and {CMRH} methods for linear systems with multiple right-hand sides", journal = NUMALGO, volume = "26", number = "4", year = "2001", pages = "317-332" } @article{hee2005, author = "M. Heyouni and A. Essai", title = "Matrix {Krylov} subspace methods for linear systems with multiple right-hand sides", journal = NUMALGO, volume = "40", number = "2", year = "2005", pages = "137-156" } @article{hys1998, author = "M. Heyouni and H. Sadok", title = "On a variable smoothing procedure for {Krylov} subspace methods", journal = LAA, volume = "268", year = "1998", pages = "131-149" } @article{hs2008, author = "M. Heyouni and H. Sadok", title = "A new implementation of the {CMRH} method for solving dense linear systems", journal = JCAM, volume = "213", number = "22", year = "2008", pages = "387-399" } @article{hz2010, author = "J. E. Hicken and D. W. Zingg", title = "A simplified and flexible variant of {GCROT} for solving nonsymmetric linear systems", journal = SISC, volume = "32", number = "3", year = "2010", pages = "1672-1694" } @inproceedings{hlb2001, author = "Y. Hida and X. S. Li and D. H. Bailey", title = "Algorithms for quad-double precision floating point arithmetic", booktitle = "Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15", year = "2001", pages = "155-162" } @article{hid1995, author = "D. J. Higham", title = "Condition numbers and their condition numbers", journal = LAA, volume = "214", year = "1995", pages = "193-213" } @article{hi1986, author = "N. J. Higham", title = "Computing the polar decomposition-with applications", journal = SISSC, volume = "7", number = "4", year = "1986", pages = "1160-1174" } @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{hi1987b, author = "N. J. Higham", title = "Error analysis of the {Bj{\"{o}}rck}-{Pereyra} algorithms for solving {Vandermonde} systems", journal = NUMAT, volume = "50", number = "5", year = "1987", pages = "613-632" } @article{hi1988, author = "N. J. Higham", title = "Algorithm 674: {FORTRAN} codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation", journal = TOMS, volume = "14", number = "4", year = "1988", pages = "381-396" } @article{hi1988b, author = "N. J. Higham", title = "Computing a nearest symmetric positive semidefinite matrix", journal = LAA, volume = "103", year = "1988", pages = "103-118" } @article{hi1988c, author = "N. J. Higham", title = "Matrix nearness problems and applications", journal = "Inst. Math. Appl. Conf. Ser. New Ser.", volume = "22", year = "1988", pages = "1-27" } @article{hi1988d, author = "N. J. Higham", title = "Fast solution of {Vandermonde}-like systems involving orthogonal polynomials", journal = IMAJNA, volume = "8", year = "1988", pages = "473-486" } @inproceedings{hi1989b, author = "N. J. Higham", title = "How accurate is {Gauss}ian 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{hi1989, author = "N. J. Higham", title = "The accuracy of solutions to triangular systems", journal = SINUM, volume = "26", number = "5", year = "1989", pages = "252-265" } @article{hi1990b, author = "N. J. Higham", title = "Bounding the error in {Gauss}ian elimination for tridiagonal systems", journal = SIMAX, volume = "11", number = "4", year = "1990", pages = "521-530" } @article{hi1990, author = "N. J. Higham", title = "Experience with a matrix norm estimator", journal = SISSC, volume = "11", year = "1990", pages = "804-809" } @article{hi1991, author = "N. J. Higham", title = "Algorithm 694: {A} collection of test matrices in {MATLAB}", journal = TOMS, volume = "17", number = "3", year = "1991", pages = "289-305" } @article{hi1992, author = "N. J. Higham", title = "Estimating the matrox $p$-norm", journal = NUMAT, volume = "62", year = "1992", pages = "539-555" } @article{hi1993, author = "N. J. Higham", title = "Perturbation theory and backward error for {$AX-XB=C$}", journal = BIT, volume = "33", year = "1993", pages = "124-136" } @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" } @article{hi1994, author = "N. J. Higham", title = "The matrix sign decomposition and its relation to the polar decomposition", journal = LAA, volume = "212", year = "1994", pages = "3-20" } @techreport{hi1995, author = {N. J. Higham}, title = {The test matrix toolbox for {Matlab}}, year = {1995}, number = {Numerical Analysis 276}, institution = {Dept. of Mathematics, University of Manchester}, } @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" } @article{hi1997b, author = "N. J. Higham", title = "Iterative refinement for linear systems and {LAPACK}", journal = IMAJNA, volume = "17", number = "4", year = "1997", pages = "495-509" } @book{hi1998, author = "N. J. Higham", title = "Handbook of Writing for the Mathematical Sciences", publisher = "SIAM", edition = "2nd", year = "1998" } @article{hi2000, author = "N. J. Higham", title = "{QR} factorization with complete pivoting and accurate computation of the {SVD}", journal = LAA, volume = "309", year = "2000", pages = "153-174" } @book{hi2002, author = "N. J. Higham", title = "Accuracy and Stability of Numerical Algorithms", edition = "2nd", publisher = "SIAM", address = "Philadelphia", year = "2002" } @article{hi2004, author = "N. J. Higham", title = "The numerical stability of barycentric {Lagrange} interpolation", journal = IMAJNA, volume = "24", number = "4", year = "2004", pages = "547-556" } @article{hi2008, author = "N. J. Higham", title = "Cayley, {Sylvester}, and early matrix theory", journal = LAA, volume = "428", year = "2008", pages = "39-43" } @book{hi2008b, author = "N. J. Higham", title = "Functions of Matrices: {T}heory and Computation", publisher = "SIAM", address = "Philadelphia", year = "2008" } @article{hi2009, author = "N. J. Higham", title = "Cholesky factorization", journal = "Wiley Interdisciplinary Reviews: Computational Statistics", volume = "1", number = "2", year = "2009", pages = "251-254" } @article{hi2011, author = "N. J. Higham", title = "Gaussian elimination", journal = "Wiley Interdisciplinary Reviews: Computational Statistics", volume = "3", number = "3", year = "2011", pages = "230-238" } @techreport{hi2013, author = "N. J. Higham", title = "Functions of matrices", institution = "The University of Manchester", number = "MIMS EPrint 2013.27", year = "2013" } @article{hi2014, author = "N. J. Higham", title = "Sylvester's influence on applied mathematics", journal = MT, volume = "50", number = "4", year = "2014", pages = "202-206" } @techreport{hi2015, author = "N. J. Higham", title = "Numerical linear algebra and matrix analysis", institution = "The University of Manchester", number = "MIMS EPrint 2015.103", year = "2015" } @techreport{hi2015b, author = "N. J. Higham", title = "Programming languages: {A}n applied mathematics view", institution = "The University of Manchester", number = "MIMS EPrint 2015.89", year = "2015" } @techreport{hi2019, author = "N. J. Higham", title = "Error analysis for standard and {GMRES}-based iterative refinement in two and three-precisions", institution = "The University of Manchester", number = "MIMS EPrint 2019.19", year = "2019" } @book{hi2020, author = "N. J. Higham", title = "Handbook of Writing for the Mathematical Sciences", publisher = "SIAM", edition = "3rd", year = "2020" } @techreport{hi2021b, author = "N. J. Higham", title = "Numerical stability of algorithms at extreme scale and low precisions", institution = "The University of Manchester", number = "MIMS EPrint 2021.14", year = "2021" } @article{hi2021, author = "N. J. Higham", title = "The mathematics of floating-point arithmetic", journal = "LMS Newsletter", volume = "493", year = "2021", pages = "35-41" } @article{hiam2010b, author = "N. J. Higham and A. {Al-Mohy}", title = "Computing matrix functions", journal = ACTNUM, volume = "19", year = "2010", pages = "159-208" } @article{hiam2010, author = "N. J. Higham and A. {Al-Mohy}", title = "The complex step approximation to the {Fr{\'{e}}chet} derivative of a matrix function", journal = NUMALGO, volume = "53", number = "1", year = "2010", pages = "133-148" } @techreport{hide2016, author = "N. J. Higham and E. Deadman", title = "A catalogue of software for matrix functions. {V}ersion 2.0.", institution = "The University of Manchester", number = "MIMS EPrint: 2016.3", year = "2016" } @article{hihi1989, author = "N. J. Higham and D. J. Higham", title = "Large growth factors in {Gaussian} 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" } @book{hihi2005, author = "N. J. Higham and D. J. Higham", title = "Matlab Guide", publisher = "SIAM", edition = "2nd", year = "2005" } @book{hihi2017, author = "N. J. Higham and D. J. Higham", title = "Matlab Guide", publisher = "SIAM", edition = "3rd", year = "2017" } @article{hhp2021, author = "N. J. Higham and D. J. Higham and S. Pranesh", title = "Random matrices generating large growth in {LU} factorization with pivoting", journal = SIMAX, volume = "42", number = "1", year = "2021", pages = "185-201" } @techreport{hiho2020, author = "N. J. Higham and E. Hopkins", title = "A catalogue of software for matrix functions. {V}ersion 3.0.", institution = "The University of Manchester", number = "MIMS EPrint: 2020.7", year = "2020" } @incollection{hili2013, author = "N. J. Higham and L. Lijing", title = "Matrix functions: {A} short course", booktitle = "Matrix Functions and Matrix Equations", editor = "Z. Bai and W. Gao and Y. Su", publisher = "Higher Education Press", year = "2013", pages = "1-27" } @article{him2019b, author = "N. J. Higham and T. Mary", title = "A new approach to probabilistic rounding error analysis", journal = SISC, volume = "41", number = "5", year = "2019", pages = "A2815-A2835" } @article{him2019, author = "N. J. Higham and T. Mary", title = "A new preconditioner that exploits low-rank approximations to factorization error", journal = SISC, volume = "41", number = "1", year = "2019", pages = "A59-A82" } @article{him2020, author = "N. J. Higham and T. Mary", title = "Sharper probabilistic backward error analysis for basic linear algebra kernels with random data", journal = SISC, volume = "42", number = "5", pages = "A3427-A3446", year = "2020" } @article{him2022, author = "N. J. Higham and T. Mary", title = "Solving block low-rank linear systems by {LU} factorization is numerically stable", journal = IMAJNA, volume = "42", number = "2", pages = "951-980", year = "2022" } @article{him2022b, author = "N. J. Higham and T. Mary", title = "Mixed precision algorithms in numerical linear algebra", journal = ACTNUM, volume = "31", year = "2022", pages = "347-414" } @article{hmt2010, author = "N. J. Higham and C. Mehl and F. Tisseur", title = "The canonical generalized polar decomposition", journal = SIMAX, volume = "31", number = "4", year = "2010", pages = "2163-2180" } @article{hino2016, author = "N. J. Higham and V. Noferini", title = "An algorithm to compute the polar decomposition of a 3x3 matrix", journal = NUMALGO, volume = "73", number = "2", pages = "349-369", year = "2016" } @inproceedings{hp1994, author = "N. J. Higham and P. Papadimitriou", title = "A new parallel algorithm for computing the singular value decomposition", booktitle = "Proceedings of the Fifth SIAM Conference on Applied Linear Algebra", publisher = "SIAM", year = "1994" } @article{hp1994b, author = "N. J. Higham and P. Papadimitriou", title = "A parallel algorithm for computing the polar decomposition", journal = PARCOMP, volume = "20", number = "8", year ="1994", pages = "1161-1173" } @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" } @article{hipr2019, author = "N. J. Higham and S. Pranesh", title = "Simulating low precision floating-point arithmetic", journal = SISC, volume = "41", number = "5", year ="2019", pages = "C585-C602" } @article{hipr2021, author = "N. J. Higham and S. Pranesh", title = "Exploiting lower precision arithmetic in solving symmetric positive definite linear systems and least squares problems", journal = SISC, volume = "43", number = "1", year ="2021", pages = "A258-A277" } @article{hpz2019, author = "N. J. Higham and S. Pranesh and M. Zounon", title = "Squeezing a matrix into half precision, with an application to solving linear systems", journal = SISC, volume = "41", number = "4", year ="2019", pages = "A2536-A2551" } @article{hir2014, author = "N. J. Higham and S. Relton", title = "Estimating the condition number of the {Fr{\'{e}}chet} derivative of a matrix function", journal = SISC, volume = "36", number = "6", year = "2014", pages = "C617-C634" } @article{hir2016, author = "N. J. Higham and S. Relton", title = "Estimating the largest elements of a matrix", journal = SISC, volume = "38", number = "5", year = "2016", pages = "C584-C601" } @article{hs1990, author = "N. J. Higham and R. S. Schreiber", title = "Fast polar decomposition of an arbitrary matrix", journal = SISSC, volume = "11", number = "4", year = "1990", pages = "648-655" } @techreport{hshe2022, author = "N. J. Higham and D. Sherwood", title = "Hamilton's discovery of the quaternions and creativity in mathematics", institution = "University of Manchester", number = "MIMS EPrint: 2022.9", year = "2022" } @article{hstr2016, author = "N. J. Higham and N. Strabi{\'{c}}", title = "Anderson acceleration of the alternating projections method for computing the nearest correlation matrix", journal = NUMALGO, volume = "72", number = "4", year = "2016", pages = "1021-1042" } @article{htvd2002, author = "N. J. Higham and F. Tisseur and P. {Van Dooren}", title = "Detecting a definite {Hermitian} pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems", journal = LAA, volume = "351", year = "2002", pages = "455-474" } @misc{hbt1904, author = "D. Hilbert", title = "Grundz{\"{u}}ge einer allgemeinen theorie der linearen integralgleichungen", howpublished = "Nachrichten von d. K{\"{o}}nigl. Ges. d. Wissensch. zu G{\"{o}}ttingen", year = "1904", pages = "49-91" } @book{hld1974, author = "F. B. Hildebrand", title = "Introduction to Numerical Analysis", publisher = "McGraw-Hill Book Company", edition = "2nd", year = "1974", note = "First edition 1956" } @article{hp1992, author = "R. O. {Hill Jr.} and B. N. Parlett", title = "Refined interlacing properties", journal = SIMAX, volume = "13", number = "1", year = "1992", pages = "239-247" } @book{hil1986, author = "W. D. Hillis", title = "The {Connnection} {Machine}", publisher = "MIT Press", year= "1986" } @article{hit1913, author = "H. Hilton", title = "Some properties of symmetric and orthogonal substitutions", journal = PLMS, volume = "2", number = "1", year = "1913", pages = "94-99" } @article{hca2005, author = "J. B. Hiriart-Urruty and H. Caussinus", title = "Sarrus, {Borel}, {Deltheil}, le {R}ouergue et ses math{\'{e}}maticiens", journal = "Gazette de la SMF", volume = "104", year = "2005", pages = "89-97" } @article{huse2010, author = "J. B. Hiriart-Urruty and A. Seeger", title = "A variational approach to copositive matrices", journal = SIREV, volume = "52", number = "4", year = "2010", pages = "593-629" } @article{hito2002, author = "J. B. Hiriart-Urruty and M. Torki", title = "Permanently going back and forth between the ``quadratic world'' and the ``convexity world'' in optimization", journal = "Appl. Math. Optim.", volume = "45", year = "2002", pages = "169-184" } @article{hir1902, author = "A. Hirsch", title = "Sur les racines d'une {\'{e}}quation fondamentale: extrait d'une lettre de {M. A. Hirsch {\`a} M. I. Bendixson}", journal = ACTM, volume = "25", year = "1902", pages = "367-370" } @article{hit1922, author = "F .L. 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