Improved rigorous perturbation bounds for the LU and QR factorizations

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 Stehle in the paper entitled “Rigorous perturbation bounds of some matrix factorizations”. This fact is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

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