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.

http://i.stanford.edu/pub/cstr/reports/cs/tr/70/162/CS-TR-70-162.pdf