Milestones in Matrix Computation

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