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Milestones in matrix computation : selected works of Gene H. Golub, with commentaries

Author: Gene H Golub; Raymond H Chan; Chen Greif; Dianne P O'Leary
Publisher: New York : Oxford University Press, 2007.
Edition/Format:   eBook : EnglishView all editions and formats

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. Including commentaries by leading  Read more...


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Genre/Form: Electronic books
Material Type: Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Gene H Golub; Raymond H Chan; Chen Greif; Dianne P O'Leary
OCLC Number: 646790545
Description: 1 online resource (xi, 565 p., [3] leaves of plates) : ill. (some col.)
Contents: GENE H GOLUB ; Biography ; Publications of Gene H. Golub ; Major Awards ; Students of Gene H. Golub ; ITERATIVE METHODS FOR LINEAR SYSTEMS ; Commentary ; References ; Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II ; A generalized conjugate gradient method for non-symmetric systems of linear equations ; A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations ; Hermitian and Skew-Hermitian splitting methods for non-Hermitian positive definite linear systems ; SOLUTION OF LEAST SQUARES PROBLEMS ; Commentary ; References ; Numerical methods for solving linear least squares problems ; Singular value decomposition and least squares solutions ; The differentiation of pseudo-inverses and non-linear least squares problems whose variables separate ; Generalized cross-validation as a method for choosing a good ridge parameter ; An analysis of the total least squares problem ; MATRIX FACTORIZATIONS AND APPLICATIONS ; Commentary ; References ; Calculating the singular values and pseudo-inverse of a matrix ; The simplex method of linear programming using LU decomposition ; On direct methods for solving Poisson's equation ; Numerical methods for computing angles between linear subspaces ; Methods for modifying matrix factorizations ; ORTHOGONAL POLYNOMIALS AND QUADRATURE ; Commentary ; References ; Calculation of Gauss quadrature rules ; Matrices, moments and quadrature ; Computation of Gauss-Kronrod quadrature rules ; EIGENVALUE PROBLEMS ; Commentary ; References ; Some modified matrix eigenvalue problems ; Ill-conditioned eigensystems and the computation of the Jordan canonical form ; The block Lanczos method for computing eigenvalues ; The numerically stable reconstruction of a Jacobi matrix from spectral data
Responsibility: Raymond H. Chan, Chen Greif, Dianne P. O'Leary.
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This collection of works by Gene H. Golub offers a wonderful insight into his contributions to the mathematical community. Jan Mayer

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