Milestones in Matrix Computation: The selected works of Gene H. Golub with commentariesRaymond Chan, Chen Greif, Dianne O'Leary OUP Oxford, 22 de febr. 2007 - 584 pàgines 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. |
Continguts
Publications of Gene H Golub | 13 |
Major Awards | 30 |
References | 43 |
A generalized conjugate gradient method | 68 |
A generalized conjugate gradient method for the numerical | 79 |
Hermitian and SkewHermitian Splitting Methods | 102 |
Commentary by Ake Bjorck | 129 |
References | 141 |
Numerical methods for computing angles between linear | 292 |
Methods for modifying matrix factorizations with | 309 |
Commentary by Walter Gautschi | 345 |
Calculation of Gauss quadrature rules with | 359 |
Matrices moments and quadrature with Gerard | 380 |
Computation of GaussKronrod Quadrature Rules with | 434 |
EIGENVALUE PROBLEMS | 452 |
465 | |
Numerical methods for solving linear least | 148 |
Singular value decomposition and least squares solutions | 160 |
The differentiation of pseudoinverses and nonlinear least | 181 |
Generalized crossvalidation as a method for choosing | 202 |
Commentary by Nicholas Higham | 227 |
The simplex method of linear programming using | 257 |
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Appl applications approximation bidiagonal calculation Chebyshev semi-iterative method coefficients columns components Concus conjugate gradient method convergence cyclic defined determine diagonal elements eigenvalue problem eigenvectors error estimate example formula function G. H. Golub Gauss rule Gauss-Kronrod quadrature Gene Golub Gene H given hence Hermitian HSS iteration IHSS ill-conditioned inverse iterative methods J. H. Wilkinson Jacobi matrix Lanczos algorithm least squares problems least squares solution Lemma Linear Algebra linear equations linear least squares linear systems Math Mathematics Matrix Anal methods for solving minimizer MODIFYING MATRIX nodes non-symmetric nonlinear norm obtain optimal orthogonal matrix orthogonal polynomials orthonormal paper parameters perturbation Poisson's equation positive definite procedure pseudo-inverse quadrature rules rank recurrence rule Nit=l Section sequence SIAM singular value decomposition spectral Stanford step subspace system of linear Theorem TLS problem total least squares transformations triangular tridiagonal matrix unitary vectors of grade weights zero