Milestones in Matrix Computation: The selected works of Gene H. Golub with commentaries

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Overview

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, Ake Bjorkc, 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.

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Product Details

  • ISBN-13: 9780199206810
  • Publisher: Oxford University Press
  • Publication date: 4/19/2007
  • Pages: 584
  • Product dimensions: 9.20 (w) x 6.20 (h) x 1.60 (d)

Table of Contents

Gene H Golub
Biography, Chen Greif
Publications of Gene H. Golub Major Awards Students of Gene H. Golub
Iterative Methods for Linear Systems
Commentary, Anne Greenbaum
References Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II, G Golub and R S Varga
A generalized conjugate gradient method for non-symmetric systems of linear equations, P Concus and G Golub
A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations, P Concus, G Golub, D O'Leary
Hermitian and Skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, Z-Z Bai, G Golub, M K Ng
Solution of Least Squares Problems
Commentary, Ake Bjorck
References Numerical methods for solving linear least squares problems, G Golub
Singular value decomposition and least squares solutions, G Golub and C Reinsch
The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate, G Golub and V Pereyra
Generalized cross-validation as a method for choosing a good ridge parameter, G Golub, M Heath, G Wahba
An analysis of the total least squares problem, G Golub and C Van Loan
Matrix Factorizations and Applications
Commentary, Nicholas Higham
References Calculating the singular values and pseudo-inverse of a matrix, G Golub and W Kahan
The simplex method of linear programming using LU decomposition, R Bartels and G Golub
On direct methods for solving Poisson's equation, B L Buzbee, G Golub, C W Nielson
Numerical methods for computing angles between linear subspaces, A Bjorck, G Golub
Methods for modifying matrix factorizations, P Gill, G Golub, W Murray, M Saunders
Orthogonal Polynomials and Quadrature
Commentary, Walter Gautschi
References Calculation of Gauss quadrature rules, G Golub, J Welsch
Matrices, moments and quadrature, G Golub, G Meurant
Computation of Gauss-Kronrod quadrature rules, D Calvetti, G Golub, W Gragg, L Reichel
Eigenvalue Problems
Commentary, G W Stewart
References Some modified matrix eigenvalue problems, G Golub
Ill-conditioned eigensystems and the computation of the Jordan canonical form, G Golub, J Wilkinson
The block Lanczos method for computing eigenvalues, G Golub, R Underwood
The numerically stable reconstruction of a Jacobi matrix from spectral data, C de Boor, G Golub

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