On the perturbation of the Q-factor of the QR factorization
Article first published online: 11 MAY 2011
Copyright © 2011 John Wiley & Sons, Ltd.
Numerical Linear Algebra with Applications
Volume 19, Issue 3, pages 607–619, May 2012
How to Cite
Chang, X.-W. (2012), On the perturbation of the Q-factor of the QR factorization. Numer. Linear Algebra Appl., 19: 607–619. doi: 10.1002/nla.787
- Issue published online: 11 APR 2012
- Article first published online: 11 MAY 2011
- Manuscript Accepted: 7 MAR 2011
- Manuscript Revised: 22 FEB 2011
- Manuscript Received: 1 JAN 2011
- QR factorization;
- perturbation analysis
This paper gives normwise and componentwise perturbation analyses for the Q-factor of the QR factorization of the matrix A with full column rank when A suffers from an additive perturbation. Rigorous perturbation bounds are derived on the projections of the perturbation of the Q-factor in the range of A and its orthogonal complement. These bounds overcome a serious shortcoming of the first-order perturbation bounds in the literature and can be used safely. From these bounds, identical or equivalent first-order perturbation bounds in the literature can easily be derived. When A is square and nonsingular, tighter and simpler rigorous perturbation bounds on the perturbation of the Q-factor are presented. Copyright © 2011 John Wiley & Sons, Ltd.