An error analysis of a method for solving matrix equations

Abstract

Let B = [ L 0 ] Q 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 B x = b Bx = b , using L but not Q, in the following manner: solve L y = b Ly = b , solve L T w = y {L^T}w = y , and form x = B T w 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.