Report Number: CS-TR-70-162
Institution: Stanford University, Department of Computer Science
Title: Numerical techniques in mathematical programming
Author: Bartels, Richard H.
Author: Golub, Gene H.
Author: Saunders, Michael A.
Date: May 1970
Abstract: The application of numerically stable matrix decompositions to minimization problems involving linear constraints is discussed and shown to be feasible without undue loss of efficiency. Part A describes computation and updating of the product-form of the LU decomposition of a matrix and shows it can be applied to solving linear systems at least as efficiently as standard techniques using the product-form of the inverse. Part B discusses orthogonalization via Householder transformations, with applications to least squares and quadratic programming algorithms based on the principal pivoting method of Cottle and Dantzig. Part C applies the singular value decomposition to the nonlinear least squares problem and discusses related eigenvalue problems.