Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T08:10:01.718Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected], [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

[1]Barrland, A., “Perturbation bounds for the LDL H and the LU factorizations”, BIT 31 (1991) 358–363.Google Scholar
[2]Chang, X.-W. and Paige, C. C., “On the sensitivity of the LU factorization”, BIT 38 (1998) 486–501.Google Scholar
[3]Chang, X.-W., Paige, C. C. and Stewart, G. W., “Perturbation analyses for the QR factorization”, SIAM J. Matrix Anal. Appl. 18 (1997) 775–791.CrossRefGoogle Scholar
[4]Dopico, F. M. and Molera, J. M., “Perturbation theory of factorizations of LU type through series expansions”, SIAM J. Matrix Anal. Appl. 27 (2005) 561–581.Google Scholar
[5]Higham, N. J., Accuracy and stability of numerical algorithms (SIAM, Philadelphia, PA, 1996).Google Scholar
[6]Singer, S. and Singer, S., “Rounding-error perturbation bounds for the indefinite QR factorization”, Linear Algebra Appl. 309 (2000) 103–119.Google Scholar
[7]Stewart, G. W., “On the perturbation of LU, Cholesky, and QR factorizations”, SIAM J. Matrix Anal. Appl. 14 (1993) 1141–1145.CrossRefGoogle Scholar
[8]Stewart, G. W., “On the perturbation of LU and Cholesky factors”, IMA J. Numer. Anal. 17 (1997) 1–6.Google Scholar
[9]Sun, J.-G., “Perturbation bounds for the Cholesky and QR factorizations”, BIT 31 (1991) 341–352.Google Scholar
[10]Sun, J.-G., “On perturbation bounds for the QR factorization”, Linear Algebra Appl. 215 (1995) 95–112.Google Scholar