Milestones in Matrix Computation The selected

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.

Biography
Publications
Major Awards
Students of
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
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Milestones in Matrix Computation The selected works of Gene H. Golub with commentaries

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