@string{ACTNUM = "Acta Numerica"}
@string{ADCM = "Adv. Comput. Math."}
@string{AJM = "Amer. J. Math."}
@string{ASEN = "Ann. Sci. Ecole Norm. Sup. Paris"}
@string{BITNM = "BIT Numerical Mathematics"}
@string{CMMP = "Comput. Math. Math. Phys."}
@string{CACM = "Comm. ACM"}
@string{CMAP = "Comp. Math. App."}
@string{CPC = "Comput. Phys. Comm."}
@string{CRAS = "C.R. Acad. Sci. Paris, S{\'{e}}r 1"}
@string{DAN = "Doklady Akademii Nauk SSSR"}
@string{ETNA = "Electron. Trans. Numer. Anal."}
@string{ITPA = "IEEE Trans. Pattern Anal. Machine Intell."}
@string{IMAJNA = "IMA J. Numer. Anal."}
@string{IPL = "Inverse Probl."}
@string{JACM = "J. ACM"}
@string{JCAM = "J. Comput. Appl. Math."}
@string{JMAA = "J. Math. Anal. Appl."}
@string{JMPA = "J. Math. Pures Appl."}
@string{JNBS = "J. Res. Natl. Bur. Stand."}
@string{JSC = "J. Sci. Comput."}
@string{LAA = "Linear Algebra Appl."}
@string{MATCOMP = "Math. Comput."}
@string{MSB = "Mat. Sb."}
@string{NLAA = "Numer. Linear Algebra Appl."}
@string{NUMALGO = "Numer. Algorithms"}
@string{NUMAT = "Numer. Math."}
@string{PAMM = "Proc. Appl. Math. Mech."}
@string{QAM = "Quart. Appl. Math."}
@string{RMJM = "Rocky Mountain J. Math."}
@string{SIAMJ = "J. Soc. Ind. Appl. Math."}
@string{SIMAX = "SIAM J. Matrix Anal. Appl."}
@string{SINUM = "SIAM J. Numer. Anal."}
@string{SISC = "SIAM J. Sci. Comput."}
@string{SISSC = "SIAM J. Sci. Statist. Comput."}
@string{SIREV = "SIAM Rev."}
@string{SMI = "Surv. Math. Ind."}
@string{TEC = "Technometrics" }
@string{TOMS = "ACM Trans. Math. Soft. (TOMS)"}
@string{ZAMP = "Z. Angew. Math. Phys."}


@article{ado1995,
 author = "{H.-M.} Adorf",
 title = "{Hubble Space Telescope} image restoration in its fourth year",
 journal = IPL,
 volume = "11",
 year = "1995",
 pages = "639-653" }

@article{aeeg2007,
 author = "M. Afanasjew and M. Eiermann and O. G. Ernst and S. G{\"{u}}ttel",
 title = "On the steepest descent method for matrix functions",
 journal = ETNA,
 volume = "28",
 year = "2007",
 pages = "206-222" }

@article{aeeg2008,
 author = "M. Afanasjew and M. Eiermann and O. G. Ernst and S. G{\"{u}}ttel",
 title = "Implementation of a restarted {K}rylov subspace method for the evaluation of matrix functions",
 journal = LAA,
 volume = "429",
 number = "10",
 year = "2008",
 pages = "2293-2314" }

@book{akh1965,
 author = "N. I. Akhiezer",
 title = "The Classical Moment Problem",
 publisher = "Oliver and Boyd",
 address = "London",
 year = "1965",
 note = "Russian edition 1961" }

@article{all1974,
 author = "D. M. Allen",
 title = "The relationship between variable selection and data augmentation and a method for prediction",
 journal = TEC,
 volume = "16",
 year = "1974",
 pages = "125-127" }

@article{acr1999,
 author = "G. S. Ammar and D. Calvetti and L. Reichel",
 title = "Computation of {Gauss-Kronrod} quadrature rules with non-positive weights",
 journal = ETNA,
 volume = "9",
 year = "1999",
 pages = "26-38" }

@article{apn1983,
 author = "A. I. Aptekarev and E. M. Nikishin",
 title = "The scattering problem for a discrete {Sturm-Liouville} operator",
 journal = MSB,
 volume = "163",
 year = "1983",
 pages = "327-358",
 note = "Also Math. USSR Sb., v.~49 (1984), pp.~325-355" }

@article{arg1988,
 author = "P. Arbenz and G. H. Golub",
 title = "On the spectral decomposition of {H}ermitian matrices modified by low rank perturbations with applications",
 journal = SIMAX,
 volume = "9",
 year = "1988",
 pages = "40-58" }

@article{ar2004,
 author = "M. Arioli",
 title = "A stopping criterion for the conjugate gradient algorithm in a finite element method framework",
 journal = NUMAT,
 volume = "97",
 year = "2004",
 pages = "1-24" }

@article{alw2005,
 author = "M. Arioli and D. Loghin and A. Wathen",
 title = "Stopping criteria for iterations in finite element methods",
 journal = NUMAT,
 volume = "99",
 year = "2005",
 pages = "381-410" }

@article{ar1951,
 author = "W. E. Arnoldi",
 title = "The principle of minimized iterations in the solution of the matrix eigenvalue problem",
 journal = QAM,
 volume = "9",
 year = "1951",
 pages = "17-29" }

@article{aru1992,
 author = "K. S. Arun",
 title = "A unitarily constrained total least squares problem in signal processing",
 journal = SIMAX,
 volume = "13",
 number = "3",
 year = "1992",
 pages = "729-745" }

@book{atk1964,
 author = "F. V. Atkinson",
 title = "Discrete and Continuous Boundary Problems",
 publisher = "Academic Press",
 address = "New York",
 year = "1964" }

@article{au1992,
 author = "G. Auchmuty",
 title = "A posteriori error estimates for linear equations",
 journal = NUMAT,
 volume = "61",
 number = "1",
 year = "1992",
 pages = "1-6" }

@article{bago1997,
 author = "Z. Bai and G. H. Golub",
 title = "Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices",
 journal = "Annals Numer. Math.",
 volume = "4",
 year = "1997",
 pages = "29-38" }

@proceedings{bago1999,
 author = "Z. Bai and G. H. Golub",
 title = "Some unusual matrix eigenvalue problems",
 booktitle = "Proceedings of Vecpar'98 -  Third International Conference for Vector and Parallel Processing",
 editor = "J. Palma and J. J. Dongarra and V. Hernandez",
 publisher = "Springer",
 address = "Berlin",
 year = "1999",
 pages = "4-19" }

@article{bfgo1996,
 author = "Z. Bai and M. Fahey and G. H. Golub",
 title = "Some large scale matrix computation problems",
 journal = JCAM,
 volume = "74",
 year = "1996",
 pages = "71-89" }

@techreport{bfgmr1998,
 author = "Z. Bai and M. Fahey and G. H. Golub and M. Menon and E. Richter",
 title = "Computing partial eigenvalue sum in electronic structure calculation",
 institution = "Stanford University",
 number = "SCCM 98-03",
 year = "1998" }

@article{baa1982,
 author = "M. M. Baart",
 title = "The use of auto-correlation for pseudo-rank determination in noisy ill-conditioned least-squares problems",
 journal = IMAJNA,
 volume = "2",
 year = "1982",
 pages = "241-247" }

@article{bad1971,
 author = "J. Baranger and M. {Duc-Jacquet}",
 title = "Matrices tridiagonales sym{\'{e}}triques et matrices factorisables",
 journal = "RIRO",
 volume = "3",
 year = "1971",
 pages = "61-66" }

@article{bjnp2006,
 author = "J. Bardsley and S. Jefferies and J. Nagy and R. J. Plemmons",
 title = "Blind iterative restoration of images with spatially-varying blur",
 journal = "Opt. Express",
 volume = "14",
 year = "2006",
 pages = "1767-1782" }

@article{bb1983,
 author = "S. Basu and N. K. Bose",
 title = "Matrix {S}tieltjes series and network models",
 journal = "SIAM J. Math. Anal.",
 volume = "14",
 number = "2",
 year = "1983",
 pages = "209-222" }

@article{bec1996,
 author = "B. Beckermann",
 title = "The stable computation of formal orthogonal polynomials",
 journal = NUMALGO,
 volume = "11",
 number = "1",
 year = "1996",
 pages = "1-23" }

@article{bec2000,
 author = "B. Beckermann",
 title = "The condition number of real {V}andermonde, {K}rylov and positive definite {H}ankel matrices",
 journal = NUMAT,
 volume = "85",
 year = "2000",
 pages = "553-577" }

@article{becb1998,
 author = "B. Beckermann and B. Bourreau",
 title = "How to choose modified moments?",
 journal = JCAM,
 volume = "98",
 year = "1998",
 pages = "81-98" }

@article{bkm2002,
 author = "M. Belge and M. E. Kilmer and E. L. Miller",
 title = "Efficient determination of multiple regularization parameters in a generalized {L}-curve framework",
 journal = IPL,
 volume = "18",
 year = "2002",
 pages = "1161-1183" }

@article{bg1999,
 author = "M. Benzi and G. H. Golub",
 title = "Bounds for the entries of matrix functions with applications to preconditioning",
 journal = BITNM,
 volume = "39",
 number = "3",
 year = "1999",
 pages = "417-438" }

@article{bra2007,
 author = "M. Benzi and N. Razouk",
 title = "Decay bounds and {O(N)} algorithms for approximating functions of sparse matrices",
 journal = ETNA,
 volume = "28",
 year = "2007",
 pages = "16-39" }

@article{ber1994,
 author = "M. Berman",
 title = "Automated smoothing of image and other regularly spaced data",
 journal = ITPA,
 volume = "16",
 year = "1994",
 pages = "460-468" }

@book{bj1996,
 author = "\AA. Bj{\"o}rck",
 title = "Numerical Methods for Least squares Problems",
 publisher = "SIAM",
 year = "1996" }

@article{bog1987,
 author = "D. L. Boley and G. H. Golub",
 title = "A survey of matrix inverse eigenvalue problems",
 journal = IPL,
 volume = "3",
 year = "1987",
 pages = "595-622" }

@phdthesis{bty2003,
 author = "G. Boutry",
 title = "Contributions {\`a} l'approximation et {\`a} l'alg{\`e}bre lin{\'e}aire num{\'e}\-rique",
 school = "Universit{\'e} des Sciences et Technologies de Lille",
 year = "2003" }

@misc{bty2007,
 author = "G. Boutry",
 title = "Construction of orthogonal polynomial wavelets as inverse eigenvalue problem and a new construction of {Gauss-Kronrod} matrices",
 howpublished = "Unpublished manuscript",
 year = "2007" }

@book{br1980,
 author = "C. Brezinski",
 title = "Pad{\'{e}}-type Approximation and General Orthogonal Polynomials",
 volume = "ISNM 50",
 publisher = "Birkh{\"a}user, Basel",
 year = "1980" }

@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" }

@book{br1992,
 author = "C. Brezinski",
 title = "Biorthogonality and its Applications to Numerical Analysis",
 publisher = "Marcel Dekker",
 address = "New York",
 year = "1992" }

@article{br1999,
 author = "C. Brezinski",
 title = "Error estimates for the solution of linear systems",
 journal = SISC,
 volume = "21",
 year = "1999",
 pages = "764-781" }

@article{brs1991,
 author = "C. Brezinski and M. Redivo-Zaglia and H. Sadok",
 title = "Avoiding breakdown and near-breakdown in {L}anczos type algorithms",
 journal = NUMALGO,
 volume = "1",
 year = "1991",
 pages = "261-284" }

@article{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{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{bud2007,
 author = "M. I. Bueno and F. M. Dopico",
 title = "A more accurate algorithm for computing the {C}hristoffel transformation",
 journal = JCAM,
 volume = "205",
 number = "1",
 year = "2007",
 pages = "567-582" }

@article{bum2004,
 author = "M. I. Bueno and F. Marcell\'{a}n",
 title = "Darboux transformation and perturbation of linear functionals",
 journal = LAA,
 volume = "384",
 year = "2004",
 pages = "215-242" }

@article{buni1978,
 author = "J. R. Bunch and C. P. Nielsen",
 title = "Updating the singular value decomposition",
 journal = NUMAT,
 volume = "31",
 year = "1978",
 pages = "111-129" }

@article{bunis1978,
 author = "J. R. Bunch and C. P. Nielsen and D. C. Sorensen",
 title = "Rank-one modification of the symmetric eigenproblem",
 journal = NUMAT,
 volume = "31",
 year = "1978",
 pages = "31-48" }

@article{bwep1996,
 author = "K. Burrage and A. Williams and J. Ehrel and B. Pohl",
 title = "The implementation of a generalized cross-validation algorithm using deflation techniques for linear systems",
 journal = "J. Appl. Numer. Math.",
 volume = "19",
 year = "1996",
 pages = "17-31" }

@article{cr2003b,
 author = "D. Calvetti and L. Reichel",
 title = "Gauss quadrature applied to trust region computations",
 journal = NUMALGO,
 volume = "34",
 year = "2003",
 pages = "85-102" }

@article{cal2003,
 author = "D. Calvetti and L. Reichel",
 title = "Tikhonov regularization of large linear problems",
 journal = BITNM,
 volume = "43",
 number = "2",
 year = "2003",
 pages = "263-283" }

@article{cr2003c,
 author = "D. Calvetti and L. Reichel",
 title = "Symmetric {Gauss-Lobatto} and modified anti-{G}auss rules",
 journal = BITNM,
 volume = "43",
 year = "2003",
 pages = "541-554" }

@article{cr2004,
 author = "D. Calvetti and L. Reichel",
 title = "Tikhonov regularization with a solution constraint",
 journal = SISC,
 volume = "26",
 number = "1",
 year = "2004",
 pages = "224-239" }

@article{cgr1999b,
 author = "D. Calvetti and G. H. Golub and L. Reichel",
 title = "Estimation of the {L}-curve via {L}anczos bidiagonalization",
 journal = BITNM,
 volume = "39",
 number = "4",
 year = "1999",
 pages = "603-619" }

@article{cgr1999,
 author = "D. Calvetti and G. H. Golub and L. Reichel",
 title = "A computable error bound for matrix functionals",
 journal = JCAM,
 volume = "103",
 year = "1999",
 pages = "301-306" }

@article{chr2002,
 author = "D. Calvetti and P. C. Hansen and L. Reichel",
 title = "L-curve curvature bounds via {L}anczos bidiagonalization",
 journal = ETNA,
 volume = "14",
 year = "2002",
 pages = "20-35" }

@inproceedings{crs1999,
 author = "D. Calvetti and L. Reichel and F. Sgallari",
 title = "Application of anti-{G}auss quadrature rules in linear algebra",
 booktitle = "Applications and Computation of Orthogonal Polynomials",
 editor = "W. Gautschi and G. H. Golub and G. Opfer",
 publisher = "Birkh{\"{a}}user",
 address = "Basel",
 year = "1999",
 pages = "41-56" }

@article{crs2004,
 author = "D. Calvetti and L. Reichel and F. Sgallari",
 title = "Tikhonov regularization with nonnegativity constraint",
 journal = ETNA,
 volume = "18",
 year = "2004",
 pages = "153-173" }

@article{crsh2005,
 author = "D. Calvetti and L. Reichel and A. Shuibi",
 title = "Tikhonov regularization of large symmetric problems",
 journal = NLAA,
 volume = "12",
 number = "2-3",
 year = "2005",
 pages = "127-139" }

@article{crsh2004b,
 author = "D. Calvetti and L. Reichel and A. Shuibi",
 title = "L-curve and curvature bounds for {T}ikhonov regularization",
 journal = NUMALGO,
 volume = "35",
 number = "2-4",
 year = "2004",
 pages = "301-314" }

@article{csr2005,
 author = "D. Calvetti and S. M. Kim and L. Reichel",
 title = "Quadrature rules based on the {A}rnoldi process",
 journal = SIMAX,
 volume = "26",
 number = "3",
 year = "2005",
 pages = "765-781" }

@article{cggr2000,
 author = "D. Calvetti and G. H. Golub and W. B. Gragg and L. Reichel",
 title = "Computation of {Gauss-Kronrod} quadrature rules",
 journal = MATCOMP,
 volume = "69",
 number = "231",
 year = "2000",
 pages = "1035-1052" }

@article{cmrs2000,
 author = "D. Calvetti and S. Morigi and L. Reichel and F. Sgallari",
 title = "Computable error bounds and estimates for the conjugate gradient method",
 journal = NUMALGO,
 volume = "25",
 year = "2000",
 pages = "79-88" }

@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{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{cpl1859,
 author = "P. L. Chebyshev",
 title = "Sur l'interpolation par la m{\'e}thode des moindres carr{\'e}s",
 journal = "M{\'e}m.~Acad.~Imp{\'e}r.~Sci. St. P{\'e}tersbourg",
 volume = "7",
 number = "15",
 year = "1859",
 pages = "1-24",
 note = "Also in {\OE}uvres I, pp.~473-498" }

@book{chi1978,
 author = "T. S. Chihara",
 title = "An Introduction to Orhogonal Polynomials",
 publisher = "Gordon and Breach",
 address = "New York",
 year = "1978" }

@article{chi2001,
 author = "T. S. Chihara",
 title = "45 years of orthogonal polynomials: a view from the wings",
 journal = JCAM,
 volume = "133",
 year = "2001",
 pages = "13-21" }

@article{cnol2008,
 author = "J. Chung and J. G. Nagy and D. P. {O'Leary}",
 title = "A weighted-{GCV} method for {L}anczos-hybrid regularization",
 journal = ETNA,
 volume = "28",
 year = "2008",
 pages = "149-167" }

@article{clcu1960,
 author = "C. W. Clenshaw and A. R. Curtis",
 title = "A method for numerical integration on an automatic computer",
 journal = NUMAT,
 volume = "2",
 year = "1960",
 pages = "197-205" }

@inproceedings{cgol1976,
 author = "P. Concus and G. H. Golub and D. P. {O{'}Leary}",
 title = "A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations",
 booktitle = "Sparse Matrix Computations",
 editor = "J. R. Bunch and D. J. Rose",
 publisher = "Academic Press",
 year = "1976",
 pages = "309-332" }

@article{ccjm1963,
 author = "P. Concus and D. Cassat and G. Jaehnig and E. Melby",
 title = "Tables for the evaluation of $\int_0^\infty x^\beta e^{-x}f(x)dx$ by {Gauss-Laguerre} quadrature",
 journal = MATCOMP,
 volume = "17",
 year = "1963",
 pages = "245-256" }

@article{cwa1979,
 author = "P. Craven and G. Wahba",
 title = "Smoothing noisy data with spline functions",
 journal = NUMAT,
 volume = "31",
 number = "4",
 year = "1979",
 pages = "377-403" }

@article{cup1981,
 author = "J. J. M. Cuppen",
 title = "A divide and conquer method for the symmetric tridiagonal eigenproblem",
 journal = NUMAT,
 volume = "36",
 number = "2",
 year = "1981",
 pages = "177-195" }

@article{cuy1997,
 author = "A. Cuyt",
 title = "Floating-point versus symbolic computations in the {QD}-algorithm",
 journal = "J. Symbolic Comput.",
 volume = "24",
 year = "1997",
 pages = "695-703" }

@book{db1974,
 author = "G. Dahlquist and \AA. Bj{\"{o}}rck",
 title = "Numerical Methods",
 publisher = "Prentice-Hall",
 year = "1974" }

@book{db2008,
 author = "G. Dahlquist and \AA. Bj{\"{o}}rck",
 title = "Numerical Methods in Scientific Computing, volume I",
 publisher = "SIAM",
 year = "2008" }

@article{deg1972,
 author = "G. Dahlquist and S. C. Eisenstat and G. H. Golub",
 title = "Bounds for the error of linear systems of equations using the theory of moments",
 journal = JMAA,
 volume = "37",
 year = "1972",
 pages = "151-166" }

@inproceedings{dgn1978,
 author = "G. Dahlquist and G. H. Golub and S. G. Nash",
 title = "Bounds for the error in linear systems",
 booktitle = "Proceedings of the Workshop on Semi-infinite Programming",
 editor = "R. Hettich",
 publisher = "Springer",
 address = "Berlin",
 year = "1978",
 pages = "154-172" }

@book{dav1989,
 author = "P. J. Davis",
 title = "The Thread: A Mathematical Yarn",
 publisher = "Harcourt Brace Jovanovich",
 address = "Boston",
 year = "1989" }

@book{pra1984,
 author = "P. J. Davis and P. Rabinowitz",
 title = "Methods of Numerical Integration",
 publisher = "Academic Press",
 year = "1984" }

@article{dbg1978,
  author = "C. {de Boor} and G. H. Golub",
  title = "The numerically stable reconstruction of a {Jacobi} matrix from spectral data",
  journal = LAA,
  volume = "21",
  number = "3",
  year = "1978",
  pages =  "245-260" }

@article{dest2002,
 author = "H. Dette and W. J. Studden",
 title = "Matrix measures, moment spaces and {F}avard's theorem for the interval $[0,1]$ and $[0,\infty)$",
 journal = LAA,
 volume = "345",
 year = "2002",
 pages = "169-193" }

@article{dest2002b,
 author = "H. Dette and W. J. Studden",
 title = "A note on the matrix q-d algorithm and matrix orthogonal polynomials on $[0,1]$ and $[0,\infty)$",
 journal = JCAM,
 volume = "148",
 year = "2002",
 pages = "349-361" }

@article{dest2003,
 author = "H. Dette and W. J. Studden",
 title = "Quadrature formulas for matrix measure - a geometric approach",
 journal = LAA,
 volume = "364",
 year = "2003",
 pages = "33-64" }

@phdthesis{dis1997,
 author = "I. S. Dhillon",
 title = "A new {O}($n^2$) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem",
 school = "EECS Department, University of California, Berkeley",
 year = "1997" }

@article{dhp2000,
 author = "I. S. Dhillon and B. N. Parlett",
 title = "Relatively robust representations of symmetric tridiagonals",
 journal = LAA,
 volume = "309",
 year = "2000",
 pages = "121-151" }

@article{dhp2004,
 author = "I. S. Dhillon and B. N. Parlett",
 title = "Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices",
 journal = LAA,
 volume = "387",
 year = "2004",
 pages = "1-28" }

@article{dhpv2006,
 author = "I. S. Dhillon and B. N. Parlett and C. V{\"{o}}mel",
 title = "The design and implementation of the {MRRR} algorithm",
 journal = TOMS,
 volume = "32",
 number = "4",
 year = "2006",
 pages = "533-560" }

@article{dhpv2005,
 author = "I. S. Dhillon and B. N. Parlett and C. V{\"{o}}mel",
 title = "Glued matrices and the {MRRR} algorithm",
 journal = SISC,
 volume = "27",
 number = "2",
 year = "2005",
 pages = "496-510" }

@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" }

@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" }

@book{dra1983,
 author = "A. Draux",
 title = "Polyn{\^o}mes Orthogonaux Formels. Applications",
 volume = "LNM 974",
 publisher = "Springer-Verlag",
 year = "1983" }

@article{dk1989,
 author = "V. Druskin and L. Knizhnerman",
 title = "Two polynomial methods of calculating functions of symmetric matrices",
 journal = CMMP,
 volume = "29",
 number = "6",
 year = "1989",
 pages = "112-121" }

@article{dk1991,
 author = "V. Druskin and L. Knizhnerman",
 title = "Error bounds for the simple {L}anczos process when computing functions of symmetric matrices and eigenvalues",
 journal = CMMP,
 volume = "31",
 number = "7",
 year = "1991",
 pages = "970-983" }

@article{dk1995,
 author = "V. Druskin and L. Knizhnerman",
 title = "Krylov space approximations of eigenpairs and matrix functions in exact and computer arithmetic",
 journal = NLAA,
 volume = "2",
 number = "3",
 year = "1995",
 pages = "205-217" }

@article{dk1998,
 author = "V. Druskin and L. Knizhnerman",
 title = "Extended {K}rylov subspace: {A}pproximation of the matrix square root and related functions",
 journal = SIMAX,
 volume = "19",
 number = "3",
 year = "1998",
 pages = "755-771" }

@article{dgk1998,
 author = "V. Druskin and A. Greenbaum and L. Knizhnerman",
 title = "Using nonorthogonal {L}anczos vectors in the computation of matrix functions",
 journal = SISC,
 volume = "19",
 number = "1",
 year = "1998",
 pages = "38-54" }

@article{ehr2002,
 author = "S. Ehrich",
 title = "On stratified extensions of {Gauss-Laguerre} and {Gauss-Hermite} quadrature formulas",
 journal = JCAM,
 volume = "140",
 year = "2002",
 pages = "291-299" }

@article{eer2006,
 author = "M. Eiermann and O. G. Ernst",
 title = "A restarted {K}rylov subspace method for the evaluation of matrix functions",
 journal = SINUM,
 volume = "44",
 number = "6",
 year = "2006",
 pages = "2481-2504" }

@article{elka1992,
 author = "S. Elhay and J. Kautsky",
 title = "Generalized {Kronrod Patterson} type embedded quadratures",
 journal = "Aplikace Matematiky",
 volume = "37",
 year = "1992",
 pages = "81-103" }

@article{elka1994,
 author = "S. Elhay and J. Kautsky",
 title = "Jacobi matrices for measures modified by a rational factor",
 journal = NUMALGO,
 volume = "6",
 year = "1994",
 pages = "205-227" }

@article{egk1991,
 author = "S. Elhay and G. H. Golub and J. Kautsky",
 title = "Updating and downdating of orthogonal polynomials with data fitting applications",
 journal = SIMAX,
 volume = "12",
 number = "2",
 year = "1991",
 pages = "327-353" }

@article{egk1992,
 author = "S. Elhay and G. H. Golub and J. Kautsky",
 title = "Jacobi matrices for sums of weight functions",
 journal = BITNM,
 volume = "32",
 year = "1992",
 pages = "143-166" }

@article{eng1993,
 author = "H. W. Engl",
 title = "Regularization methods for the stable solution of inverse problems",
 journal = SMI,
 volume = "3",
 number = "4",
 year = "1993",
 pages = "71-143" }

@article{fas1995,
 author = "D. Fasino",
 title = "Spectral properties of {H}ankel matrices and numerical solutions of finite moment problems",
 journal = JCAM,
 volume = "65",
 year = "1995",
 pages = "145-155" }

@article{fav1935,
 author = "J. Favard",
 title = "Sur les polyn{\^o}mes de {T}chebicheff",
 journal = CRAS,
 volume = "200",
 year = "1935",
 pages = "2052-2053" }

@article{fer1997,
 author = "K. V. Fernando",
 title = "On computing an eigenvector of a tridiagonal matrix. {Part I}: basic results",
 journal = SIMAX,
 volume = "18",
 number = "4",
 year = "1997",
 pages = "1013-1034" }

@article{fp1994,
 author = "K. V. Fernando and B. N. Parlett",
 title = "Accurate singular values and differential qd algorithms",
 journal = NUMAT,
 volume = "67",
 year = "1994",
 pages = "191-229" }

@techreport{fpd1995,
 author = "K. V. Fernando and B. N. Parlett and I. S. Dhillon",
 title = "A way to find the most redundant equation in a tridiagonal system",
 institution = "Center for Pure and Applied Mathematics, University of California",
 address = "Berkeley",
 number = "PAM-635",
 year = "1995" }

@article{fghol1997,
 author = "R. D. Fierro and G. H. Golub and P. C. Hansen and D. P. {O'Leary}",
 title = "Regularization by truncated total least squares",
 journal = SISC,
 volume = "18",
 number = "4",
 year = "1997",
 pages = "1223-1241" }

@book{fis1996,
 author = "B. Fischer",
 title = "Polynomial Based Iteration Methods for Symmetric Linear Systems",
 publisher = "Wiley Teubner",
 year = "1996" }

@article{fig1991,
 author = "B. Fischer and G. H. Golub",
 title = "On generating polynomials which are orthogonal over several intervals",
 journal = MATCOMP,
 volume = "56",
 number = "194",
 year = "1991",
 pages = "711-730" }

@inproceedings{fig1993,
 author = "B. Fischer and G. H. Golub",
 title = "On the error computation for polynomial based iteration methods",
 booktitle = "Recent Advances in Iterative Methods",
 editor = "A. Greenbaum and M. Luskin",
 publisher = "Springer",
 address = "New York",
 year = "1994",
 pages = "59-67" }

@inproceedings{fl1976,
 author = "R. Fletcher",
 title = "Conjugate gradient methods for indefinite systems",
 booktitle = "Numerical Analysis. Lecture Notes in Mathematics, vol 506",
 editor = "G. A. Watson",
 publisher = "Springer",
 address = "Berlin, Heidelberg",
 year = "1976",
 pages = "73-89" }

@article{for1957,
 author = "G. E. Forsythe",
 title = "Generation and use of orthogonal polynomials for data fitting with a digital computer",
 journal = SIAMJ,
 volume = "5",
 year = "1957",
 pages = "74-88" }

@inproceedings{fh1993,
 author = "R.W. Freund and M. Hochbruck",
 title = "{G}auss quadratures associated with the {A}rnoldi process and the {L}anczos algorithm",
 booktitle = "Linear Algebra for Large Scale and Real-time Applications",
 editor = "M. S. Moonen and G. H. Golub and B. {De Moor}",
 publisher = "Kluwer",
 year = "1993",
 pages = "377-380" }

@article{fgn1993,
 author = "R. W. Freund and M. H. Gutknecht and N. M. Nachtigal",
 title = "An implementation of the look-ahead {L}anczos algorithm for non-{H}ermitian matrices",
 journal = SISC,
 volume = "14",
 year = "1993",
 pages = "137-158" }

@article{frma1999,
 author = "A. Frommer and P. Maas",
 title = "Fast {CG}-based methods for {Tikhonov-Phillips} regularization",
 journal = SISC,
 volume = "20",
 year = "1999",
 pages = "1831-1850" }

@incollection{fsi2008,
 author = "A. Frommer and V. Simoncini",
 title = "Matrix functions",
 booktitle = "Model Order Reduction: Theory, Research Aspects and Applications",
 editor = "W. H. A. Schilders and H. A. van der Vorst and J. Rommes",
 note = "Volume 13 of Mathematics in Industry",
 publisher = "Springer",
 year = "2008",
 pages = "275-304" }

@article{gal1971,
 author = "D. Galant",
 title = "An implementation of {C}hristoffel's theorem in the theory of orthogonal polynomials",
 journal = MATCOMP,
 volume = "25",
 year = "1971",
 pages = "111-113" }

@article{gal1992,
 author = "D. Galant",
 title = "Algebraic methods for modified orthogonal polynomials",
 journal = MATCOMP,
 volume = "59",
 number = "200",
 year = "1992",
 pages = "541-546" }

@article{gaw1981,
 author = "W. Gander",
 title = "Least squares with a quadratic constraint",
 journal = NUMAT,
 volume = "36",
 year = "1981",
 pages = "291-307" }

@article{ggvm1989,
 author = "W. Gander and G. H. Golub and U. {von Matt}",
 title = "A constrained eigenvalue problem",
 journal = LAA,
 volume = "114/115",
 year = "1989",
 pages = "815-839" }

@book{ga1959,
 author = "F. R. Gantmacher",
 title = "The Theory of Matrices, {V}ol. 1",
 publisher = "AMS Chelsea Publishing",
 address = "Providence, RI",
 year = "1959" }

@article{gagr1997,
 author = "K. Gates and W. B. Gragg",
 title = "Notes on {TQR} algorithms",
 journal = JCAM,
 volume = "86",
 year = "1997",
 pages = "195-203" }

@article{gauss1814,
 author = "C. F. Gauss",
 title = "Methodus nova integralium valores per approximationem inveniendi",
 journal = "Commentationes Societatis Regiae Scientarium Gottingensis Recentiores",
 volume = "3",
 year = "1814",
 pages = "39-76" }


@article{gaut1968,
 author = "W. Gautschi",
 title = "Construction of {Gauss-Christoffel} quadrature formulas",
 journal = MATCOMP,
 volume = "22",
 year = "1968",
 pages = "251-270" }

@article{gaut1970,
 author = "W. Gautschi",
 title = "On the construction of {G}aussian quadrature rules from modified moments",
 journal = MATCOMP,
 volume = "24",
 year = "1970",
 pages = "245-260" }

@article{gaut1982,
 author = "W. Gautschi",
 title = "On generating orthogonal polynomials",
 journal = SISSC,
 volume = "3",
 number = "3",
 year = "1982",
 pages = "289-317" }

@article{gaut1985,
 author = "W. Gautschi",
 title = "Orthogonal polynomials - constructive theory and applications",
 journal = JCAM,
 volume = "12-13",
 year = "1985",
 pages = "61-76" }

@article{gaut1997,
 author = "W. Gautschi",
 title = "Moments in quadrature problems",
 journal = CMAP,
 volume = "33",
 number = "1/2",
 year = "1997",
 pages = "105-118" }

@article{gaut1999,
 author = "W. Gautschi",
 title = "Orthogonal polynomials and quadrature",
 journal = ETNA,
 volume = "9",
 year = "1999",
 pages = "65-76" }

@book{gaut2004,
 author = "W. Gautschi",
 title = "Orthogonal Polynomials: Computation and Approximation",
 publisher = "Oxford University Press",
 year = "2004" }

@article{gaut2005,
 author = "W. Gautschi",
 title = "Orthogonal polynomials (in {M}atlab)",
 journal = JCAM,
 volume = "178",
 number = "1-2",
 year = "2005",
 pages = "215-234" }

@article{gaut2005b,
 author = "W. Gautschi",
 title = "A historical note on {Gauss-Kronrod} quadrature",
 journal = NUMAT,
 volume = "100",
 year = "2005",
 pages = "483-484" }

@article{gava1983,
 author = "W. Gautschi and R. S. Varga",
 title = "Error bounds for {G}aussian quadrature of analytic functions",
 journal = SINUM,
 volume = "20",
 number = "6",
 year = "1983",
 pages = "1170-1186" }

@article{gmo1982,
 author = "J. S. Geronimo",
 title = "Scattering theory and matrix orthogonal polynomials on the real line",
 journal = "Circuits Systems Signal Process.",
 volume = "1",
 year = "1982",
 pages = "471-495" }

@article{gfr1987,
 author = "H. Gfrerer",
 title = "An a posteriori parameter choice for ordinary and iterated {T}ikhonov regularization of ill-posed problems
  leading to optimal convergence rates",
 journal = MATCOMP,
 volume = "49",
 year = "1987",
 pages = "507-522" }

@inproceedings{ gwa1959,
 author = "G. Goertzel and H. V. Waldinger and J. Agresta",
 title = "The method of spherical harmonics as applied to the one-velocity {B}oltzmann equation in infinite cylinders",
 booktitle = "ACM'59, 14th national meeting of the Association for Computing Machinery",
 publisher = "ACM",
 year = "1959",
 pages = "1-5" }

@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{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{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{gok1983,
 author = "G. H. Golub and J. Kautsky",
 title = "Calculation of {G}auss quadratures with multiple free and fixed knots",
 journal = NUMAT,
 volume = "41",
 year = "1983",
 pages = "147-163" }

@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" }

@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",
 institution = "Stanford University, Computer Science Dept.",
 number = "SCCM-01-05",
 year = "2001" }

@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" }

@article{gs1994,
 author = "G. H. Golub and Z. Strako{\v{s}}",
 title = "Estimates in quadratic formulas",
 journal = NUMALGO,
 volume = "8",
 number = "2",
 year = "1994",
 pages = "241-268" }

@inproceedings{gu1977,
 author = "G. H. Golub and R. Underwood",
 title = "The block {L}anczos method for computing eigenvalues",
 booktitle = "Mathematical Software {III}, Proceedings of a Symposium conducted by the Mathematics Research Center, the University of Wisconsin-Madison, March 28{-}30, 1977",
 editor = "J. Rice",
 publisher = "Academic Press",
 year = "1977",
 pages = "361-377" }

@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{gvl1996,
 author = "G. H. Golub and C. F. {Van Loan}",
 title = "Matrix {C}omputations",
 edition = "3rd",
 publisher = "Johns Hopkins University Press",
 address = "Baltimore",
 year = "1996" }

@article{go1961,
  author = "G. H. Golub and R. S. Varga",
  title = "{Chebyshev} semi-iterative methods, successive overrelaxation iterative Methods, and second order {Richardson} iterative methods. {I}",
  journal = NUMAT,
  volume = "3",
  number = "1",
  year = "1961",
  pages = "147-156" }

@article{go1961b,
  author = "G. H. Golub and R. S. Varga",
  title = "{Chebyshev} semi-iterative methods, successive overrelaxation iterative Methods, and second order {Richardson} iterative methods. {II}",
  journal = NUMAT,
  volume = "3",
  number = "1",
  year = "1961",
  pages = "157-168" }

@article{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{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{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" }

@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{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{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{grh1984,
 author = "W. B. Gragg and W. J. Harrod",
 title = "The numerically stable reconstruction of {J}acobi matrices from spectral data",
 journal = NUMAT,
 volume = "44",
 number = "3",
 year = "1984",
 pages = "317-335" }

@techreport{grc2003,
 author = "J. F. Grcar",
 title = "Optimal sensitivity analysis of linear least squares problems",
 institution = "Lawrence Berkeley National Laboratory",
 number = "LBNL-52434",
 year = "2003" }

@article{gbcw1989,
 author = "C. Gu and D. M. Batres and Z. Chen and G. Wahba",
 title = "The computation of generalized cross-validation functions through {H}ouseholder tridiagonalization
  with applications to the fitting of interaction spline models",
 journal = SIMAX,
 volume = "10",
 number = "4",
 year = "1989",
 pages = "457-480" }

@article{gue1995b,
 author = "M. Gu and S. C. Eisenstat",
 title = "A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem",
 journal = SIMAX,
 volume = "16",
 number = "1",
 year = "1995",
 pages = "172-191" }

@article{hdm1892,
 author = "J. Hadamard",
 title = "Essai sur l'{\'{e}}tude des fonctions donn{\'{e}}es par leur d{\'{e}}veloppement de {T}aylor",
 journal = JMPA,
 volume = "4{\`e}me s{\'{e}}rie, 8",
 year = "1892",
 pages = "101-186" }

@article{hnk1996,
 author = "M. Hanke",
 title = "Limitations of the {L}-curve method in ill-posed problems",
 journal = BITNM,
 volume = "36",
 number = "2",
 year = "1996",
 pages = "287-301" }

@inproceedings{hnk2000,
 author = "M. Hanke",
 title = "Iterative regularization techniques in image restoration",
 booktitle = "Surveys on Solution Methods for Inverse Problems",
 editor = "D. Colton and H. W. Engl and A. K. Louis and J. R. McLaughlin and W. Rundell",
 publisher = "Springer-Verlag",
 address = "Berlin",
 year = "2000",
 pages = "35-52" }

@article{hnk2001,
 author = "M. Hanke",
 title = "On {L}anczos based methods for the regularization of discrete ill-posed problems",
 journal = BITNM,
 volume = "41",
 number = "5",
 year = "2001",
 pages = "1008-1018" }

@article{hnk2003,
 author = "M. Hanke",
 title = "A note on {T}ikhonov regularization of large linear problems",
 journal = BITNM,
 volume = "43",
 year = "2003",
 pages = "449-451" }

@article{hha1993,
 author  = "M. Hanke and P. C. Hansen",
 title = "Regularization methods for large scale problems",
 journal = SMI,
 volume = "3",
 number = "4",
 year = "1993",
 pages = "253-315" }

@article{hna1996,
 author = "M. Hanke and J. G. Nagy",
 title = "Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques",
 journal = IPL,
 volume = "12",
 year = "1996",
 pages = "157-173" }

@article{har1996,
 author = "M. Hanke and T. Raus",
 title = "A general heuristic for choosing the regularization parameter in ill-posed problems",
 journal = SISC,
 volume = "17",
 number = "4",
 year = "1996",
 pages = "956-972" }

@article{hpc1992,
 author = "P. C. Hansen",
 title = "Analysis of discrete ill-posed problems by means of the {L}-curve",
 journal = SIREV,
 volume = "34",
 number = "4",
 year = "1992",
 pages = "561-580" }

@article{hpc1994,
 author = "P. C. Hansen",
 title = "Regularization tools: a {M}atlab package for analysis and solution of discrete ill-posed problems",
 journal = NUMALGO,
 volume = "6",
 number = "1",
 year = "1994",
 pages = "1-35" }

@book{hpc1998,
 author = "P. C. Hansen",
 title = "Rank-deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion",
 publisher = "SIAM",
 year = "1998" }

@article{hpc2007,
 author = "P. C. Hansen",
 title = "{Regularization Tools} version 4.0 for {Matlab 7.3}",
 journal = NUMALGO,
 volume = "46",
 number = "2",
 year = "2007",
 pages = "189-194" }

@article{hol1993,
 author = "P. C. Hansen and D. P. {O'Leary}",
 title = "The use of the {L}-curve in the regularization of discrete ill-posed problems",
 journal = SISC,
 volume = "14",
 number = "6",
 year = "1993",
 pages = "1487-1503" }

@article{hjr2007,
 author = "P. C. Hansen and T. K. Jensen and G. Rodriguez",
 title = "An adaptive pruning algorithm for the discrete {L}-curve criterion",
 journal = JCAM,
 volume = "198",
 number = "2",
 year = "2007",
 pages = "483-492" }

@article{hay1984,
 author = "R. Haydock",
 title = "Comparison of quadrature and termination for estimating the density of states within the recursion method",
 journal = "J. Phys. C: Solid State Phys.",
 volume = "17",
 year = "1984",
 pages = "4783-4789" }

@article{hay1989,
 author = "R. Haydock",
 title = "Accuracy of the recursion method and basis non-orthogonality",
 journal = CPC,
 volume = "53",
 year = "1989",
 pages = "133-139" }

@article{hayt1994,
 author = "R. Haydock and R. L. Te",
 title = "Accuracy of the recursion method",
 journal = "Phys. Rev. B: Condensed Matter",
 volume = "49",
 year = "1994",
 pages = "10845-10850" }

@incollection{hen1958,
 author = "P. Henrici",
 title = "The quotient difference algorithm",
 booktitle = "NBS Appl. Math. Series, 49",
 publisher = "National Bureau of Standards",
 year = "1958",
 pages = "23-46" }

@incollection{hen1967,
 author = "P. Henrici",
 title = "Quotient-difference algorithms",
 booktitle = "Mathematical Methods for Digital Computers",
 editor = "A. Ralston and H. S. Wilf",
 publisher = "J. Wiley",
 address = "New York",
 year = "1967",
 pages = "37-62" }

@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" }

@book{hi2002,
 author = "N. J. Higham",
 title = "Accuracy and Stability of Numerical Algorithms",
 edition = "2nd",
 publisher = "SIAM",
 address = "Philadelphia",
 year = "2002" }

@book{hi2008b,
 author = "N. J. Higham",
 title = "Functions of Matrices: {T}heory and Computation",
 publisher = "SIAM",
 address = "Philadelphia",
 year = "2008" }

@article{hns2007,
 author = "I. Hn\v{e}tynkov{\`a} and Z. Strako\v{s}",
 title = "Lanczos tridiagonalization and core problems",
 journal = LAA,
 volume = "421",
 year = "2007",
 pages = "243-251" }

@techreport{hoho2006,
 author = "M. Hochbruck and M. Hochstenbach",
 title = "Subspace extraction for matrix functions",
 institution = "Heinrich-Heine-Universit{\"a}t D{\"u}sseldorf",
 number = "?",
 year = "2006" }

@article{hl1997,
 author = "M. Hochbruck and C. Lubich",
 title = "On {K}rylov subspace approximations to the matrix exponential operator",
 journal = SINUM,
 volume = "34",
 number = "5",
 year = "1997",
 pages = "1911-1925" }

@book{ho1964,
 author = "A. S. Householder",
 title = "The Theory of Matrices in Numerical Analysis",
 publisher = "Blaisdell",
 address = "New York",
 year = "1964",
 note = "Reprinted by Dover, New York, (1975)" }

@article{hut1986,
 author = "M. Hutchinson",
 title = "Algorithm 642: a fast procedure for calculating minimum cross-validation cubic smoothing spline",
 journal = TOMS,
 volume = "12",
 year = "1986",
 pages = "150-153" }

@article{hut1989,
 author = "M. Hutchinson",
 title = "A stochastic estimator of the trace of the influence matrix for {L}aplacian smoothing splines",
 journal = "Comm.~Statist.~Simul.",
 volume = "18",
 year = "1989",
 pages = "1059-1076" }

@article{hudh1985,
 author = "M. Hutchinson and F. R. {De Hoog}",
 title = "Smoothing noisy data with spline functions",
 journal = NUMAT,
 volume = "47",
 year = "1985",
 pages = "99-106" }

@misc{ipl2005,
 author = "I. C. F. Ipsen and D. J. Lee",
 title = "Determinant approximation",
 howpublished = "arXiv preprint arXiv:1105.0437",
 year = "2005" }

@article{kky1981,
 author = "J. Kautsky",
 title = "Matrices related to interpolatory quadrature",
 journal = NUMAT,
 volume = "36",
 year = "1981",
 pages = "309-318" }

@article{kky1992,
 author = "J. Kautsky",
 title = "Gauss quadratures: {A}n inverse problem",
 journal = SIMAX,
 volume = "13",
 number = "1",
 year = "1992",
 pages = "402-417" }

@article{kyey1982,
 author = "J. Kautsky and S. Elhay",
 title = "Calculation of the weights of interpolatory quadratures",
 journal = NUMAT,
 volume = "40",
 year = "1982",
 pages = "407-422" }

@article{kyey1984,
 author = "J. Kautsky and S. Elhay",
 title = "Gauss quadratures and {J}acobi matrices for weight functions not of one sign",
 journal = MATCOMP,
 volume = "43",
 year = "1984",
 pages = "543-550" }

@article{kygo1983,
 author = "J. Kautsky and G. H. Golub",
 title = "On the calculation of {J}acobi matrices",
 journal = LAA,
 volume = "52/53",
 year = "1983",
 pages = "439-455" }

@article{kiol2001,
 author = "M. E. Kilmer and D. P. {O'Leary}",
 title = "Choosing regularization parameter in iterative methods for ill-posed problems",
 journal = SIMAX,
 volume = "22",
 number = "4",
 year = "2001",
 pages = "1204-1221" }

@article{kis1999,
 author = "M. E. Kilmer and G. W. Stewart",
 title = "Iterative regularization and {MINRES}",
 journal = SIMAX,
 volume = "21",
 number = "2",
 year = "1999",
 pages = "613-628" }

@article{kn1991,
 author = "L. Knizhnerman",
 title = "Calculation of functions of unsymmetric matrices using {A}rnoldi's method",
 journal = CMMP,
 volume = "31",
 number = "1",
 year = "1992",
 pages = "1-9" }

@article{kn1996,
 author = "L. Knizhnerman",
 title = "The simple {L}anczos procedure: estimates of the error of the {G}auss quadrature formula and their applications",
 journal = CMMP,
 volume = "36",
 number = "11",
 year = "1996",
 pages = "1481-1492" }

@article{kn2008,
 author = "L. Knizhnerman",
 title = "Gauss-{A}rnoldi quadrature for {$ \bigl\langle(zI-A)^{-1}\varphi,\,\varphi\bigr\rangle$} and rational
  {P}ad{\'e}-type approximation for {M}arkov-type functions",
 journal = MSB,
 volume = "199",
 year = "2008",
 pages = "185-206" }

@article{kre1949,
 author = "M. G. Krein",
 title = "Fundamental aspects of the representation theory of {H}ermitian operators with deficiency index (m, m)",
 journal = "Ukrain. Mat. Z.",
 volume = "1",
 year = "1949",
 pages = "3-66",
 note = "Amer. Math. Soc. Transl., v.~2 n.~97 (1970), pp.~75-143" }

@article{kro1964,
 author = "A. S. Kronrod",
 title = "Integration with control of accuracy",
 journal = DAN,
 volume = "154",
 year = "1964",
 pages = "283-286" }

@misc{kro1965,
 author = "A. S. Kronrod",
 title = "Nodes and weights of quadrature formulas: sixteen-place tables",
 howpublished = "Consultants Bureau, New York ",
 year = "1965" }

@article{la2005,
 author = "J. V. Lambers",
 title = "{K}rylov subspace spectral methods for variable-coefficient initial-boundary value problems",
 journal = ETNA,
 volume = "20",
 year = "2005",
 pages = "212-234" }

@article{la2007,
 author = "J. V. Lambers",
 title = "Practical implementation of {K}rylov subspace spectral methods",
 journal = JSC,
 volume = "32",
 year = "2007",
 pages = "449-476" }

@article{la2008,
 author = "J. V. Lambers",
 title = "Derivation of high-order spectral methods for time-dependent {PDE} using modified moments",
 journal = ETNA,
 volume = "28",
 year = "2008",
 pages = "114-135" }

@article{la2008b,
 author = "J. V. Lambers",
 title = "Implicitly defined high-order operator splittings for parabolic and hyperbolic variable-coefficient {PDE}
  using modified moments",
 journal = "Int. J. Comput. Science",
 volume = "2",
 year = "2008",
 pages = "376-401" }

@article{la2008c,
 author = "J. V. Lambers",
 title = "Enhancement of {K}rylov subspace spectral methods by block {L}anczos iteration",
 journal = ETNA,
 volume = "31",
 year = "2008",
 pages = "86-109" }

@article{lan1950,
 author = "C. Lanczos",
 title = "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators",
 journal = JNBS,
 volume = "45",
 year = "1950",
 pages = "255-282" }

@article{lan1952,
 author = "C. Lanczos",
 title = "Solution of systems of linear equations by minimized iterations",
 journal = JNBS,
 volume = "49",
 year = "1952",
 pages = "33-53" }

@article{lau1996,
 author = "D. P. Laurie",
 title = "Anti-{G}aussian quadrature formulas",
 journal = MATCOMP,
 volume = "65",
 number = "214",
 year = "1996",
 pages = "739-747" }

@article{lau1997,
 author = "D. P. Laurie",
 title = "Calculation of {Gauss-Kronrod} quadrature rules",
 journal = MATCOMP,
 volume = "66",
 year = "1997",
 pages = "1133-1145" }

@article{lau1999,
 author = "D. P. Laurie",
 title = "Accurate recovery of recursion coefficients from {G}aussian quadrature formulas",
 journal = JCAM,
 volume = "112",
 year = "1999",
 pages = "165-180" }

@inproceedings{lau1999b,
 author = "D. P. Laurie",
 title = "Questions related to {G}aussian quadrature formulas and two-term recursions",
 booktitle = "Applications and Computation of Orthogonal Polynomials",
 editor = "W. Gautschi and G. H. Golub and G. Opfer",
 publisher = "Birkh{\"{a}}user",
 address = "Basel",
 year = "1999",
 pages = "133-144" }

@article{lau2001,
 author = "D. P. Laurie",
 title = "Computation of {G}auss-type quadrature formulas",
 journal = JCAM,
 volume = "127",
 year = "2001",
 pages = "201-217" }

@book{lh1995,
 author = "C. L. Lawson and R. J. Hanson",
 title = "Solving Least Squares Problems",
 publisher = "SIAM",
 address = "Philadelphia",
 note = "First edition, Prentice-Hall (1974)",
 year = "1995" }

@article{leo1978,
 author = "A. S. Leonov",
 title = "On the choice of regularization parameters by means of the quasi-optimality and ratio criteria",
 journal = DAN,
 volume = "240",
 number = "1",
 year  ="1978",
 pages = "18-20" }

@article{likc1985,
 author = "K. C. Li",
 title = "From {S}tein's unbiased risk estimates to the method of generalized cross-validation",
 journal = "Annals Statist.",
 volume = "13",
 year = "1985",
 pages = "1352-1377" }

@techreport{lirc1994,
 author = "R. C. Li",
 title = "Solving secular equations stably and efficiently",
 institution = "University of California, Berkeley",
 number = "UCB CSD-94-851",
 year = "1994" }

@article{likf2000,
 author = "{K.-F. Liu}",
 title = "A noisy {Monte Carlo} algorithm with fermion determinant",
 journal = "Chinese J.~Phys.",
 volume = "38",
 year = "2000",
 pages = "605-614" }

@misc{lob1851,
 author = "R. Lobatto",
 title = "Lessen over de differentiaal - en integraal-rekening",
 howpublished = "De Gebroeders Van Cleef, 's Gravenhage and Amsterdam",
 year = "1851" }

@article{lum1992,
 author = "H. Lu and F. H. Mathis",
 title = "Surface approximation by spline smoothing and generalized cross-validation",
 journal = "Math. Comput. Simul.",
 volume = "34",
 year = "1992",
 pages = "541-549" }

@article{man2001,
 author = "F. Marcell\'{a}n and R. {Alvarez-Nodarse}",
 title = "On the {``Favard theorem''} and its extensions",
 journal = JCAM,
 volume = "127",
 number = "1-2",
 year = "2001",
 pages = "231-254" }

@article{may2002,
 author = "F. Marcell\'{a}n and H. O. Yakhlef",
 title = "Recent trends on analytic properties of matrix orthonormal polynomials",
 journal = ETNA,
 volume = "14",
 year = "2002",
 pages = "127-141" }

@article{mel1997,
 author = "A. Melman",
 title = "A unifying convergence analysis of second-order methods for secular equation",
 journal = MATCOMP,
 volume = "66",
 number = "217",
 year = "1997",
 pages = "333-344" }

@article{mel1997b,
 author = "A. Melman",
 title = "A numerical comparison of methods for solving secular equations",
 journal = JCAM,
 volume = "86",
 year = "1997",
 pages = "237-249" }

@article{gm1992,
 author = "G. Meurant",
 title = "A review on the inverse of symmetric tridiagonal and block tridiagonal matrices",
 journal = SIMAX,
 volume = "13",
 number = "3",
 year = "1992",
 pages = "707-728" }

@article{gm1997,
 author = "G. Meurant",
 title = "The computation of bounds for the norm of the error in the conjugate gradient algorithm",
 journal = NUMALGO,
 volume = "16",
 year = "1997",
 pages = "77-87" }

@article{gm1999,
 author = "G. Meurant",
 title = "Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm",
 journal = NUMALGO,
 volume = "22",
 year = "1999",
 pages = "353-365" }

@book{gm1999b,
 author = "G. Meurant",
 title = "Computer Solution of Large Linear Systems",
 publisher = "North-Holland",
 address = "Amsterdam",
 year = "1999" }

@article{gm2005,
 author = "G. Meurant",
 title = "Estimates of the $\ell_2$ norm of the error in the conjugate gradient algorithm",
 journal = NUMALGO,
 volume = "40",
 number = "2",
 year = "2005",
 pages = "157-169" }

@book{gm2006,
 author = "G. Meurant",
 title = "The {L}anczos and Conjugate Gradient Algorithms, from Theory to Finite Precision Computations",
 publisher = "SIAM",
 address = "Philadelphia",
 year = "2006" }

@article{gm2009b,
 author = "G. Meurant",
 title = " {Gene H. Golub} 1932-2007",
 journal = NUMALGO,
 volume = "51",
 number = "1",
 year = "2009",
 pages = "1-4" }

@article{gm2009,
 author = "G. Meurant",
 title = "Estimates of the trace of the inverse of a symmetric matrix using the modified {C}hebyshev algorithm",
 journal = NUMALGO,
 volume = "51",
 number = "3",
 year = "2009",
 pages = "309-318" }

@article{mz2006,
 author = "G. Meurant and Z. Strako\v{s}",
 title = "The {L}anczos and conjugate gradient algorithms in finite precision arithmetic",
 journal = ACTNUM,
 volume = "15",
 year = "2006",
 pages = "471-542" }

@article{mgo2001,
 author = "G. Monegato",
 title = "An overview of the computational aspects of {K}ronrod quadrature rules",
 journal = NUMALGO,
 volume = "26",
 year = "2001",
 pages = "173-196" }

@book{mor1984,
 author = "V. A. Morozov",
 title = "Methods for Solving Incorrectly Posed Problems",
 publisher = "Springer",
 address = "Berlin",
 year = "1984" }

@inproceedings{mume1998,
 author = "M. M{\"u}hlich and R. Mester",
 title = "The role of total least squares in motion analysis",
 booktitle = "Proceedings of the European Conference on Computer Vision",
 editor = "H. Burkhardt",
 publisher = "Springer",
 address = "Berlin",
 year = "1998",
 pages = "305-321" }

@article{npp2004,
 author = "J. G. Nagy and K. Palmer and L. Perrone",
 title = "Iterative methods for image deblurring: {A Matlab} object oriented approach",
 journal = NUMALGO,
 volume = "36",
 year = "2004",
 pages = "73-93" }

@article{nex1978,
 author = "C. M. Nex",
 title = "Estimation of integrals with respect to a density of states",
 journal = "J. Phys. A",
 volume = "11",
 number = "4",
 year = "1978",
 pages = "653-663" }

@article{nex1989,
 author = "C. M. Nex",
 title = "The block {L}anczos algorithm and the calculation of matrix resolvents",
 journal = CPC,
 volume = "53",
 year = "1989",
 pages = "141-146" }

@article{ol1980b,
 author = "D. P. {O'Leary}",
 title = "The block conjugate gradient algorithm and related methods",
 journal = LAA,
 volume = "29",
 year = "1980",
 pages = "293-322" }

@article{ol2001c,
 author = "D. P. {O'Leary}",
 title = "Near-optimal parameters for {T}ikhonov and other regularization methods",
 journal = SISC,
 volume = "23",
 number = "4",
 year = "2001",
 pages = "1161-1171" }

@article{ols1981,
 author = "D. P. {O'Leary} and J. A. Simmons",
 title = "A bidiagonalization-regularization procedure for large scale discretizations of ill-posed problems",
 journal = SISSC,
 volume = "2",
 number = "4",
 year = "1981",
 pages = "474-489" }

@article{olst2007,
 author = "D. P. {O'Leary} and Z. Strako\v{s} and P. Tich\'{y}",
 title = "On sensitivity of {Gauss-Christoffel} quadrature",
 journal = NUMAT,
 volume = "107",
 number = "1",
 year = "2007",
 pages = "147-174" }

@article{ort1989,
 author = "B. Ortner",
 title = "On the selection of measurement directions in second-rank tensor (e.g.~elastic strain) determination of
 single crystals",
 journal = "J. Appl. Cryst.",
 volume = "22",
 year = "1989",
 pages = "216-221" }

@article{okr1996,
 author = "B. Ortner and A. R. Kr{\"a}uter",
 title = "Lower bounds for the determinant and the trace of a class of {H}ermitian matrix",
 journal = LAA,
 volume = "236",
 year = "1996",
 pages = "147-180" }

@phdthesis{pai1971,
 author = "C. C. Paige",
 title = "The computation of eigenvalues and eigenvectors of very large sparse matrices",
 school = "University of London",
 address = "UK",
 year = "1971" }

@article{ps1982,
 author = "C. C. Paige and M. A. Saunders",
 title = "{LSQR}: {A}n algorithm for sparse linear equations and sparse least squares",
 journal = TOMS,
 volume = "8",
 number = "1",
 year = "1982",
 pages = "43-71" }

@article{ps1982b,
 author = "C. C. Paige and M. A. Saunders",
 title = "Algorithm 583; {LSQR}: {S}parse linear equations and least-squares problems",
 journal = TOMS,
 volume = "8",
 number = "2",
 year = "1982",
 pages = "195-209" }

@inproceedings{pst2001,
 author = "C. C. Paige and Z. Strako\v{s}",
 title = "Bounds for the least squares residual using scaled total least squares",
 booktitle = "Proceedings of the Third International Workshop on {TLS} and Error-in-variables Modelling",
 editor = "S. {Van Huffel} and P. Lemmerling",
 publisher = "Kluwer",
 address = "Dordrecht",
 year = "2001",
 pages = "25-34" }

@inproceedings{pst2001b,
 author = "C. C. Paige and Z. Strako\v{s}",
 title = "Unifying least squares, total least squares and data least squares",
 booktitle = "Proceedings of the Third International Workshop on {TLS} and Error-in-variables Modelling",
 editor = "S. {Van Huffel} and P. Lemmerling",
 publisher = "Kluwer",
 address = "Dordrecht",
 year = "2001",
 pages = "35-44" }

@article{pst2002,
 author = "C. C. Paige and Z. Strako\v{s}",
 title = "Bounds for the least squares distance using scaled total least squares",
 journal = NUMAT,
 volume = "91",
 year = "2002",
 pages = "93-115" }

@article{pst2002c,
 author = "C. C. Paige and Z. Strako\v{s}",
 title = "Scaled total least squares fundamentals",
 journal = NUMAT,
 volume = "91",
 year = "2002",
 pages = "117-146" }

@article{pst2006,
 author = "C. C. Paige and Z. Strako\v{s}",
 title = "Core problems in linear algebraic systems",
 journal = SIMAX,
 volume = "27",
 number = "3",
 year = "2006",
 pages = "861-874" }

@article{ppv1995,
 author = "C. C. Paige and B. N. Parlett and H. {van der Vorst}",
 title = "Approximate solutions and eigenvalue bounds from {K}rylov subspaces",
 journal = NLAA,
 volume = "2",
 number = "2",
 year = "1995",
 pages = "115-133" }

@article{par1964,
 author = "B. N. Parlett",
 title = "The development and use of methods of {LR} type",
 journal = SIREV,
 volume = "6",
 number = "3",
 year = "1964",
 pages = "275-295" }

@article{par1995,
 author = "B. N. Parlett",
 title = "The new qd algorithms",
 journal = ACTNUM,
 volume = "4",
 year = "1995",
 pages = "459-491" }

@book{par1980,
 author = "B. N. Parlett",
 title = "The Symmetric Eigenvalue Problem",
 publisher = "Prentice Hall",
 year = "1980",
 note = "Reprinted by SIAM (1998)" }

@article{par2000b,
 author = "B. N. Parlett",
 title = "For tridiagonals {$T$} replace {$T$} with {$LDL^T$}",
 journal = JCAM,
 volume = "123",
 number = "1-2",
 year = "2000",
 pages = "117-130" }

@article{pad1997,
 author = "B. N. Parlett and I. S. Dhillon",
 title = "Fernando's solution to {W}ilkinson's problem: {A}n application of double factorization",
 journal = LAA,
 volume = "267",
 year = "1997",
 pages = "247-279" }

@article{pam2000,
 author = "B. N. Parlett and O. A. Marques",
 title = "An implementation of the dqds algorithm (positive case)",
 journal = LAA,
 volume = "309",
 year = "2000",
 pages = "217-259" }

@article{ps1979,
 author = "B. N. Parlett and D. S. Scott",
 title = "The {L}anczos algorithm with selective orthogonalization",
 journal = MATCOMP,
 volume = "33",
 number = "145",
 year = "1979",
 pages = "217-238" }

@inproceedings{pzk1985,
 author = "S. Paszkowski",
 title = "Sur des transformations d'une fonction de poids",
 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 = "Berlin",
 year = "1985",
 pages = "239-246",
 note = "LNM v. 1171" }

@article{patt1968,
 author = "T. N. L. Patterson",
 title = "The optimal addition of points to quadrature formulae",
 journal = MATCOMP,
 volume = "22",
 year = "1968",
 pages = "847-856" }

@article{patt1993,
 author = "T. N. L. Patterson",
 title = "Modified optimal quadrature extensions",
 journal = NUMAT,
 volume = "64",
 year = "1993",
 pages = "511-520" }

@article{patt1999,
 author = "T. N. L. Patterson",
 title = "Stratified nested and related quadrature rules",
 journal = JCAM,
 volume = "112",
 year = "1999",
 pages = "243-251" }

@article{pgvr1998,
 author = "R. Pintelon and P. Guillaume and G. Vandersteen and Y. Rolain",
 title = "Analyses, development, and applications of {TLS} algorithms in frequency domain system identification",
 journal = SIMAX,
 volume = "19",
 number = "4",
 year = "1998",
 pages = "983-1004" }

@article{rad1880,
 author = "R. Radau",
 title = "Etude sur les formules d'approximation qui servent {\`a} calculer la valeur num{\'e}rique d'une int{\'e}grale d{\'e}finie",
 journal = JMPA,
 volume = "6",
 year = "1880",
 pages = "283-336" }

@article{reg1996,
 author = "T. Reg{\'{\i}}nska",
 title = "A regularization parameter in discrete ill-posed problems",
 journal = SISC,
 volume = "17",
 number = "3",
 year = "1996",
 pages = "740-749" }

@article{rei1991b,
 author = "L. Reichel",
 title = "Fast {QR} decomposition of {V}andermonde-like matrices and polynomial least squares approximation",
 journal = SIMAX,
 volume = "12",
 number = "3",
 year = "1991",
 pages = "552-564" }

@article{rei1993,
 author = "L. Reichel",
 title = "Construction of polynomials that are orthogonal with respect to a discrete bilinear form",
 journal = ADCM,
 volume = "1",
 year = "1993",
 pages = "241-258" }

@article{rrs2009,
 author = "L. Reichel and G. Rodriguez and S. Seatzu",
 title = "Error estimates for large-scale ill-posed problems",
 journal = NUMALGO,
 volume = "51",
 number = "3",
 year = "2009",
 pages = "341-361" }

@article{rsc1967,
 author = "C. Reinsch",
 title = "Smoothing with spline functions",
 journal = NUMAT,
 volume = "10",
 year = "1967",
 pages = "177-183" }

@article{rsc1971,
 author = "C. Reinsch",
 title = "Smoothing with spline functions {II}",
 journal = NUMAT,
 volume = "16",
 year = "1971",
 pages = "451-455" }

@book{rsn1990,
 author = "F. Riesz and B. {Sz-Nagy}",
 title = "Functional Analysis",
 publisher = "Dover",
 address = "New York",
 year = "1990",
 note = "Original edition published in 1952" }

@article{rg1967,
 author = "J. L. Rigal and J. Gaches",
 title = "On the compatibility of a given solution with the data of a linear system",
 journal = JACM,
 volume = "14",
 number = "3",
 year = "1967",
 pages = "543-548" }

@article{row1992,
 author = "P. D. Robinson and A. J. Wathen",
 title = "Variational bounds on the entries of the inverse of a matrix",
 journal = IMAJNA,
 volume = "12",
 year = "1992",
 pages = "463-486" }

@article{ru1954,
 author = "H. Rutishauser",
 title = "Der {Quotienten-Differenzen-Algorithmus}",
 journal = ZAMP,
 volume = "5",
 number = "3",
 year = "1954",
 pages = "233-251" }

@misc{ru1958,
 author = "H. Rutishauser",
 title = "Solution of eigenvalue problems with the {LR}-transformation",
 howpublished = "National Bureau of Standards, Applied Mathematics Series 49",
 year = "1958",
 pages = "47-81" }

@inproceedings{rut1963,
 author = "H. Rutishauser",
 title = "On {J}acobi rotation patterns",
 booktitle = "Proceedings of Symposia in Applied Mathematics, v.~15, Experimental Arithmetic, High Speed Computing and Mathematics",
 publisher = "American Mathematical Society",
 year = "1963",
 pages = "219-239" }

@article{sdo1972,
 author = "R. A. Sack and A. Donovan",
 title = "An algorithm for {G}aussian quadrature given modified moments",
 journal = NUMAT,
 volume = "18",
 number = "5",
 year = "1972",
 pages = "465-478" }

@article{szr1973,
 author = "H. E. Salzer",
 title = "A recurrence scheme for converting from one orthogonal expansion into another",
 journal = CACM,
 volume = "16",
 number = "11",
 year = "1973",
 pages = "705-707" }

@article{sgm1991,
 author = "B. Sapoval and T. Gobron and A. Margolina",
 title = "Vibrations of fractal drums",
 journal = "Phys. Rev. Lett.",
 volume = "67",
 number = "21",
 year = "1991",
 pages = "2974-2977" }

@article{ssy1998,
 author = "M. A. Saunders and H. D. Simon and E. L. Yip",
 title = "Two conjugate-gradient-type methods for unsymmetric linear equations",
 journal = SINUM,
 volume = "25",
 number = "4",
 year = "1988",
 pages = "927-940" }

@article{sm2001,
 author = "P. E. Saylor and D. C. Smolarski",
 title = "Why {G}aussian quadrature in the complex plane?",
 journal = NUMALGO,
 volume = "26",
 year = "2001",
 pages = "251-280" }

@article{sm2001b,
 author = "P. E. Saylor and D. C. Smolarski",
 title = "Addendum to: {W}hy {G}aussian quadrature in the complex plane?",
 journal = NUMALGO,
 volume = "27",
 year = "2001",
 pages = "215-217" }

@article{scu1990,
 author = "L. L. Schumaker and F. I. Utreras",
 title = "On generalized cross-validation for tensor smoothing splines",
 journal = SISSC,
 volume = "11",
 year = "1990",
 pages = "713-731" }

@techreport{sew1994,
 author = "J. C. Sexton and D. H. Weingarten",
 title = "Systematic expansion for full {QCD} based on the valence approximation",
 institution = "IBM T.J.~Watson Research Center",
 number = "?",
 year = "1994" }

@article{shan1989,
 author = "B. Shahraray and D. J. Anderson",
 title = "Optimal estimation of contour properties by cross-validated regularization",
 journal = ITPA,
 volume = "11",
 year = "1989",
 pages = "600-610" }

@article{sho1936,
 author = "J. A. Shohat",
 title = "The relation of classical orthogonal polynomials to the polynomials of {A}ppell",
 journal = AJM,
 volume = "58",
 year = "1936",
 pages = "453-464" }

@book{sht1943,
 author = "J.A.~Shohat and J.D.~Tamarkin",
 title = "The Problem of Moments",
 publisher = "American Mathematical Society",
 year = "1943",
 note = "Mathematical Surveys, v.~1" }

@inproceedings{sbp2003,
 author = "R. B. Sidje and K. Burrage and B. Philippe",
 title = "An augmented {L}anczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix",
 booktitle = "Computational Science - ICCS 2003",
 publisher = "Springer",
 address = "Berlin",
 year = "2003",
 pages = "693-704" }

@article{sivh2005,
 author = "D. M. Sima and S. {Van Huffel}",
 title = "Using core formulations for ill-posed linear systems",
 journal = PAMM,
 volume = "5",
 number = "1",
 year = "2005",
 pages = "795-796",
 note = "Proceedings of the 76th GAMM Annual Meeting" }

@article{svhg2004,
 author = "D. M. Sima and S. {Van Huffel} and G. H. Golub",
 title = "Regularized total least squares based on quadratic eigenvalue problem solvers",
 journal = BITNM,
 volume = "44",
 year = "2004",
 pages = "793-812" }

@article{shd1984,
 author = "H. D. Simon",
 title = "The {L}anczos algorithm with partial reorthogonalization",
 journal = MATCOMP,
 volume = "42",
 number = "165",
 year = "1984",
 pages = "115-142" }

@article{snp1995,
 author = "A. Sinap",
 title = "Gaussian quadrature for matrix valued functions on the real line",
 journal = JCAM,
 volume = "65",
 year = "1995",
 pages = "369-385" }

@article{siva1994,
 author = "A. Sinap and W. {Van Assche}",
 title = "Polynomial interpolation and {G}aussian quadrature for matrix-valued functions",
 journal = LAA,
 volume = "207",
 year = "1994",
 pages = "71-114" }

@article{siva1996,
 author = "A. Sinap and W. {Van Assche}",
 title = "Orthogonal matrix polynomials and applications",
 journal = JCAM,
 volume = "66",
 year = "1996",
 pages = "27-52" }

@article{skr1992,
 author = "M. R. Skrzipek",
 title = "Orthogonal polynomials for modified weight functions",
 journal = JCAM,
 volume = "41",
 year = "1992",
 pages = "331-346" }

@article{sku1894,
 author = "R. Skutsch",
 title = "{\"{U}}ber formelpaare der mechanischen quadratur",
 journal = "Arch. Math. Phys.",
 volume = "13",
 number = "2",
 year = "1894",
 pages = "78-83" }

@article{spc2007,
 author = "M. M. Spalevi\'{c}",
 title = "On generalized averaged {G}aussian formulas",
 journal = MATCOMP,
 volume = "76",
 number = "259",
 year = "2007",
 pages = "1483-1492" }

@book{st1998,
 author = "G. W. Stewart",
 title = "Matrix Algorithms, volume {I}: {B}asic Decompositions",
 publisher = "SIAM",
 address = "Philadelphia",
 year = "1998" }

@incollection{st1958,
 author = "E. Stiefel",
 title = "Kernel polynomial in linear algebra and their numerical applications",
 booktitle = "Further Contributions to the Solution of Simultaneoous Linear Equations and the Determination of Eigenvalues",
 publisher = "National Bureau of Standards, Applied Math. Ser. 49",
 year = "1958",
 pages = "1-22" }

@article{stie1884,
 author = "T. J. Stieltjes",
 title = "Quelques recherches sur la th{\'{e}}orie des quadratures dites m{\'{e}}caniques",
 journal = ASEN,
 volume = "S{\'{e}}r. 3 tome 1",
 year = "1884",
 pages = "409-426",
 note = "Also in {\OE}uvres compl{\`e}tes, vol.~1, Noordhoff, Groningen, (1914), pp.~377-396" }

@article{stie1894,
 author = "T. J. Stieltjes",
 title = "Recherches sur les fractions continues",
 journal = "Ann. Fac. Sci. Toulouse",
 volume = "9",
 number = "J1-122",
 year = "1894",
 pages = "A1-10",
 note = "Also in {\OE}uvres compl{\`e}tes, vol.~2, Noordhoff, Groningen, (1918), pp.~402-566" }

@book{sb1980,
 author = "J. Stoer and R. Bulirsch",
 title = "Introduction to Numerical Analysis",
 publisher = "Springer Verlag",
 address = "New York",
 year = "1980" }

@article{stra1991,
 author = "Z. Strako\v{s}",
 title = "On the real convergence rate of the conjugate gradient method",
 journal = LAA,
 volume = "154-156",
 year = "1991",
 pages = "535-549" }

@article{stra2009,
 author = "Z. Strako\v{s}",
 title = "Model reduction using the {V}orobyev moment problem",
 journal = NUMALGO,
 volume = "51",
 year = "2009",
 pages = "363-379" }

@article{stt2002,
 author = "Z. Strako\v{s} and P. Tich{\'y}",
 title = "On error estimation in the conjugate gradient method and why it works in finite precision computations",
 journal = ETNA,
 volume = "13",
 year = "2002",
 pages = "56-80" }

@article{stt2005,
 author = "Z. Strako\v{s} and P. Tich{\'y}",
 title = "Error estimation in preconditioned conjugate gradients",
 journal = BITNM,
 volume = "45",
 year = "2005",
 pages = "789-817" }

@article{stt2008,
 author = "Z. Strako\v{s} and P. Tich{\'y}",
 title = "On efficient numerical approximation of the bilinear form $c^* {A}^{-1}b$ ",
 journal = SISC,
 volume = "32",
 number = "2",
 year = "2008",
 pages = "565-587" }

@book{sts1966,
 author = "A. H. Stroud and D. Secrest",
 title = "Gaussian Quadrature Formulas",
 publisher = "Prentice-Hall",
 year = "1966" }

@article{sbl1963,
 author = "G. W. Struble",
 title = "Orthogonal polynomials: variable-signed weight functions",
 journal = NUMAT,
 volume = "5",
 year = "1963",
 pages = "88-94" }

@phdthesis{zhs2005,
 author = "Z. Su",
 title = "Computational methods for least squares problems and clinical trials",
 school = "Stanford University",
 year = "2005" }

@book{sze1939,
 author = "G. Szeg{\"{o}}",
 title = "Orthogonal Polynomials",
 publisher = "American Mathematical Society",
 address = "Providence, R.I.",
 year = "1939" }

@book{tik1992,
 author = "A. N. Tikhonov",
 title = "Ill-posed Problems in Natural Sciences, Proceedings of the International Conference Moscow 1991",
 publisher = "TVP Science",
 address = "Moscow",
 note = "Editor",
 year = "1992" }

@book{tia1976,
 author = "A. N. Tikhonov and V. Y. Arsenin",
 title = "Solutions of Ill-posed Problems",
 publisher = "Mir",
 address = "Moscow",
 note = " Translation to English, Wiley, 1977",
 year = "1976" }

@article{tbkt1991,
 author = "A. M. Thompson and J. C. Brown and J. W. Kay and D. M. Titterington",
 title = "A study of methods of choosing the smoothing parameter in image restoration by regularization",
 journal = ITPA,
 volume = "13",
 year = "1991",
 pages = "326-339" }

@article{tre2008,
 author = "L. N. Trefethen",
 title = "Is {G}auss quadrature better than {Clenshaw-Curtis}?",
 journal = SIREV,
 volume = "50",
 number = "1",
 year = "2008",
 pages = "67-87" }

@article{tyr1994,
 author = "E. E. Tyrtyshnikov",
 title = "How bad are {H}ankel matrices?",
 journal = NUMAT,
 volume = "67",
 year = "1994",
 pages = "261-269" }

@article{utr1980,
 author = "F. I. Utreras",
 title = "Sur le choix du param{\`e}tre d'ajustement dans le lissage par fonctions spline",
 journal = NUMAT,
 volume = "34",
 year = "1980",
 pages = "15-28" }

@article{utr1981,
 author = "F. I. Utreras",
 title = "Optimal smoothing of noisy data using spline functions",
 journal = SISSC,
 volume = "2",
 year = "1981",
 pages = "349-362" }

@article{uvv1959,
 author = "V. B. Uvarov",
 title = "Relation between polynomials orthogonal with different weights",
 journal = DAN,
 volume = "126",
 year = "1959",
 pages = "33-36",
 note = "(in Russian)" }

@article{uvv1969,
 author = "V. B. Uvarov",
 title = "The connection between systems of polynomials that are orthogonal with respect to different distribution functions",
 journal = "USSR Comput. Math. Phys.",
 volume = "9",
 year = "1969",
 pages = "25-36" }

@book{vhv1991,
 author = "S. {Van Huffel} and J. Vandewalle",
 title = "The Total Least Squares Problem: Computational Aspects and Analysis",
 publisher = "SIAM",
 address = "Philadelphia",
 year = "1991" }

@article{vah1983,
 author = "J. M. Varah",
 title = "Pitfalls in the numerical solution of linear ill-posed problems",
 journal = SISSC,
 volume = "4",
 number = "2",
 year = "1983",
 pages = "164-176" }

@article{vntw2005,
 author = "R. Vio and J. G. Nagy and L. Tenorio and W. Wamsteker",
 title = "Multiple image deblurring with spatially variant {PSF}s",
 journal = "Astron.~Astrophys.",
 volume = "434",
 year = "2005",
 pages = "795-800" }

@article{vcr1996,
 author = "C. R. Vogel",
 title = "Non-convergence of the {L}-curve regularization parameter selection method",
 journal = IPL,
 volume = "12",
 number = "4",
 year = "1996",
 pages = "535-547" }

@article{vmu1997,
 author = "U. {von Matt}",
 title = "The orthogonal qd-algorithm",
 journal = SISC,
 volume = "18",
 number = "4",
 year = "1997",
 pages = "1163-1186" }

@book{vo1965,
 author = "Y. V. Vorobyev",
 title = "Methods of Moments in Applied Mathematics",
 publisher = " Gordon and Breach Science Publishers",
 address = "New York",
 year = "1965" }

@inproceedings{wah1980,
 author = "G. Wahba",
 title = "Spline bases, regularization and generalized cross-validation for solving approximation problems
  with large quantities of noisy data",
 booktitle = "Approximation Theory III",
 editor = "E. W. Cheney",
 year = "1980",
 pages = "905-912" }

@book{wah1990,
 author = "G. Wahba",
 title = "Spline Models for Observational Data",
 publisher = "SIAM",
 address = "Philadelphia",
 year = "1990",
 note = "CBMS-NSF Regional Conference Series in Applied Mathematics" }

@article{waw1975,
 author = "G. Wahba and S. Wold",
 title = "A completely automatic {F}rench curve",
 journal = "Commun.~Statist.",
 volume = "4",
 number = "1",
 year = "1975",
 pages = "1-17" }

@article{wjgg1995,
 author = "G. Wahba and D. R. Johnson and F. Gao and J. Gong",
 title = "Adaptive tuning of numerical weather prediction models; randomized {GCV} in three and four-dimensional data assimilation",
 journal = "Mon. Weather Rev.",
 volume = "123",
 year = "1995",
 pages = "3358-3369" }

@article{wks1995,
 author = "B. Wald{\'e}n and R. Karlson and J. G. Sun",
 title = "Optimal backward perturbation bounds for the linear least squares problem",
 journal = NLAA,
 volume = "2",
 number = "3",
 year = "1995",
 pages = "271-286" }

@techreport{wck1997,
 author = "K. F. Warnick",
 title = "Continued fraction error bound for conjugate gradient method",
 institution = "ECEN Dept., Brigham Young University",
 number = "TR-L100-98.3",
 year = "1997" }

@techreport{wck2000,
 author = "K. F. Warnick",
 title = "Gaussian quadrature and scattering amplitude",
 institution = "Electrical and Computer Engineering Dept., University of Illinois",
 number = "unpublished",
 year = "2000" }

@techreport{wck2000b,
 author = "K. F. Warnick",
 title = "Nonincreasing error bound for the biconjugate gradient method",
 institution = "Electrical and Computer Engineering Dept., University of Illinois",
 number = "unpublished",
 year = "2000" }

@article{wet2007,
 author = "J. A. C. Weideman and L. N. Trefethen",
 title = "The kink phenomenon in {F}ej{\'e}r and {Clenshaw-Curtis} quadrature",
 journal = NUMAT,
 volume = "107",
 year = "2007",
 pages = "707-727" }

@article{whe1974,
 author = "J. C. Wheeler",
 title = "Modified moments and {G}aussian quadrature",
 journal = "RMJM",
 volume = "4",
 number = "2",
 year = "1974",
 pages = "287-296",
 note = "Proceedings of the International Conference on Pad{\'e} Approximants, Continued Fractions and Related Topics" }

@book{wif1962,
 author = "H. S. Wilf",
 title = "Mathematics for the Physical Sciences",
 publisher = "Wiley",
 address = "New York",
 year = "1962" }

@inproceedings{wbu1995,
 author = "A. Williams and K. Burrage",
 title = "Surface fitting using {GCV} smoothing splines on supercomputers",
 booktitle = "Conference on High Performance Networking and Computing",
 publisher = "ACM",
 year = "1995",
 note = "Proceedings of the 1995 ACM/IEEE Conference on Supercomputing" }

@article{wcj1992,
 author = "S. Y. Wu and J. A. Cocks and C. S. Jayanthi",
 title = "An accelerated inversion algorithm using the resolvent matrix method",
 journal = CPC,
 volume = "71",
 year = "1992",
 pages = "125-133" }

@article{xssm1999,
 author = "M. Xia and E. Saber and G. Sharma and A. {Murat Tekalp}",
 title = "End-to-end color printer calibration by total least squares regression",
 journal = "IEEE Trans. Image Process.",
 volume = "8",
 number = "5",
 year = "1999",
 pages = "700-716" }

@article{xsf1996,
 author = "S. F. Xu",
 title = "On the {J}acobi matrix inverse eigenvalue problem with mixed given data",
 journal = SIMAX,
 volume = "17",
 number = "3",
 year = "1996",
 pages = "632-639" }