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Improved rigorous perturbation bounds for the LU and QR factorizations
Author(s) -
Li Hanyu,
Wei Yimin
Publication year - 2015
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1998
Subject(s) - mathematics , perturbation (astronomy) , pure mathematics , quantum mechanics , physics
Summary Combining the modified matrix–vector equation approach with the technique of Lyapunov majorant function and the Banach fixed point theorem, we obtain improved rigorous perturbation bounds for the LU and QR factorizations with normwise perturbation in the given matrix. Each of the improved rigorous perturbation bounds is a rigorous version of the first‐order perturbation bound derived by the matrix–vector equation approach in the literature, and we present their explicit expressions. These bounds are always tighter than those given by Chang and Stehlé in the paper entitled “Rigorous perturbation bounds of some matrix factorizations”. This fact is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.