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基本説明
Provides a historical insight into the development of numerical Linear Algebra.
Full Description
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 is 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. Commentaries for each area are provided by leading experts: Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also included 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.
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
