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PERTURBATION THEORY FOR THE LU AND QR FACTORIZATIONS

Part of: Numerical linear algebra Basic linear algebra

Published online by Cambridge University Press:  01 April 2008

CHI-YE WU  and
TING-ZHU HUANG
CHI-YE WU
Affiliation:
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
TING-ZHU HUANG*
Affiliation:
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China (email: tingzhuhuang@126.com, tzhuang@uestc.edu.cn)
*
✉For correspondence; e-mail: tingzhuhuang@126.com
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Abstract

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In this paper we derive perturbation theorems for the LU and QR factors. Moreover, bounds for κL(A)/κL′(A) and κU(A)/κ′U(A) are given for the LU factorization of a nonsingular matrix. By applying pivoting strategies in the LU factorization, estimates for κL(PAQ)/κL′(PAQ) and κU(PAQ)/κ′U(PAQ) are also obtained.

Keywords

LU factorizationQR factorizationperturbation

MSC classification

Secondary: 15A23: Factorization of matrices 65F35: Matrix norms, conditioning, scaling
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 451 - 461
Copyright
Copyright © Australian Mathematical Society 2008

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