Perturbation theory for the LU and QR factorizations

Abstract

In this paper we derive perturbation theorems for the LU and QR factors. Moreover, bounds for $\kappa_L(A)/\kappa_L'(A)$ and $\kappa_U(A)/\kappa'_U(A)$ are given for the LU factorization of a nonsingular matrix. Applying to pivoting strategies in the LU factorization, $\kappa_L(PAQ)/\kappa_L'(PAQ)$ and $\kappa_U(PAQ)/\kappa'_U(PAQ)$ are also obtained. doi:10.1017/S1446181108000138