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
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