An Error Analysis of a Method for Solving Matrix Equations

Abstract

Let <!-- MATH $B = [L\;0]Q$ --> be a decomposition of the m by n matrix B of rank m such that L is lower triangular and Q is orthonormal. It is possible to solve , using L but not Q, in the following manner: solve , solve <!-- MATH ${L^T}w = y$ --> , and form <!-- MATH $x = {B^T}w$ --> . It is shown that the numerical stability of this method is comparable to that of the method which uses Q. This is important for some methods used in mathematical programming where B is very large and sparse and Q is discarded to save storage.