Last update: Sun Mar 31 03:12:58 MDT 2019
@Book{Chan:2007:MMC,
editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
booktitle = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
title = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 565 + 3",
year = "2007",
ISBN = "0-19-920681-3",
ISBN-13 = "978-0-19-920681-0",
LCCN = "QA188 .G67 2007",
MRclass = "65-06 (01A75 65Fxx)",
MRnumber = "MR2281939 (2008b:65004)",
MRreviewer = "David Scott Watkins",
bibdate = "Sat Apr 07 10:23:33 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/numana2000.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib;
http://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
URL = "http://www.loc.gov/catdir/enhancements/fy0737/2007276086-d.html",
abstract = "The text presents and discusses some of the most
influential papers in Matrix Computation authored by
Gene H. Golub, one of the founding fathers of the
field. The collection of 21 papers in divided into five
main areas: iterative methods for linear systems,
solution of least squares problems, matrix
factorizations and applications, orthogonal polynomials
and quadrature, and eigenvalue problems an commentaries
for each area are provided by leading experts: Anne
Greenbaum, {\AA}ke Bj{\"o}rck, Nicholas Higham, Walter
Gautschi, and G. W. (Pete) Stewart. Comments on each
paper are also provided by the original authors,
providing the reader with historical information on how
the paper came to be written and under what
circumstances the collaboration was undertaken.
Including a brief biography and facsimiles of the
original papers, this text will be of great interest to
students and researchers in numerical analysis and
scientific computation.",
acknowledgement = ack-nhfb,
tableofcontents = "List of Plates / x \\
I: Gene H. Golub \\
1 Gene H. Golub Biography, by Chen Greif / 3 \\
2 Publications of Gene H. Golub / 13 \\
3 Major Awards / 30 \\
4 Students of Gene H. Golub / 32 \\
II: Iterative Methods for Linear Systems \\
5 Commentary, by Anne Greenbaum / 35 \\
References / 43 \\
6 Chebyshev semi-iterative methods, successive
over-relaxation iterative methods, and second-order
Richardson iterative methods, Parts I and II (with R.
S. Varga) / 45 \\
7 A generalized conjugate gradient method for
non-symmetric systems of linear equations (with Paul
Concus) / 68 \\
8 A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations (with Paul Concus and Dianne P. O'Leary) / 79
\\
9 Hermitian and Skew-Hermitian Splitting Methods for
Non-Hermitian Positive Definite Linear Systems (with
Zhong-Zhi Bai and Michael K. Ng) / 102 \\
III: Solution of Least Squares Problems \\
10 Commentary, by {\AA}ke Bj{\"o}rck / 129 \\
References / 141 \\
11 Numerical methods for solving linear least squares
problems / 148 \\
12 Singular value decomposition and least squares
solutions (with C. Reinsch) / 160 \\
13 The differentiation of pseudo-inverses and
non-linear least squares problems whose variables
separate (with V. Pereyra) / 181 \\
14 Generalized cross-validation as a method for
choosing a good ridge parameter (with M. Heath and G.
Wahba) / 202 \\
15 An analysis of the total least squares problem (with
C. Van Loan) / 213 \\
IV: Matrix Factorizations and Applications \\
16 Commentary, by Nicholas Higham / 227 \\
References / 233 \\
17 Calculating the singular values and pseudo-inverse
of a matrix (with W. Kahan) / 236 \\
18 The simplex method of linear programming using $ L U
$ decomposition (with R. H. Bartels) / 257 \\
19 On direct methods for solving Poisson's equation
(with B. L. Buzbee and C. W. Nielson) / 261 \\
20 Numerical methods for computing angles between
linear subspaces (with {\AA}. Bj{\"o}rck) / 292 \\
21 Methods for modifying matrix factorizations (with P.
E. Gill, W. Murray and M. A. Saunders) / 309 \\
V: Orthogonal Polynomials and Quadrature \\
22 Commentary, by Walter Gautschi / 345 \\
References / 354 \\
23 Calculation of Gauss quadrature rules (with J. H.
Welsch) / 359 \\
24 Matrices, moments, and quadrature (with G{\'e}rard
Meurant) / 380 \\
25 Computation of Gauss--Kronrod Quadrature Rules (with
D. Calvetti, W. B. Gragg and L. Reichel) / 434 \\
VI: Eigenvalue Problems \\
26 Commentary, by G. W. Stewart / 457 \\
References / 465 \\
27 Some modified matrix eigenvalue problems / 467 \\
28 Ill-conditioned eigensystems and the computation of
the Jordan canonical form (with J. H. Wilkinson) / 485
\\
29 The block Lanczos method for computing eigenvalues
(with R. Underwood) / 528 \\
30 The numerically stable reconstruction of a Jacobi
matrix from spectral data (with C. de Boor) / 546 Index
/ 563",
}