New rigorous perturbation bounds for the generalized Cholesky factorization

TL;DR

This paper derives new, tighter perturbation bounds for the generalized Cholesky factorization, applicable to normwise and componentwise perturbations, with simple conditions for their validity.

Contribution

It introduces novel rigorous bounds that improve upon existing ones for the generalized Cholesky factorization under various perturbations.

Findings

Bounds are significantly tighter than previous results.

Applicable to both normwise and componentwise perturbations.

Conditions for bounds to hold are simple and moderate.

Abstract

Some new rigorous perturbation bounds for the generalized Cholesky factorization with normwise or componentwise perturbations in the given matrix are obtained, where the componentwise perturbation has the form of backward rounding error for the generalized Cholesky factorization algorithm. These bounds can be much tighter than some existing ones while the conditions for them to hold are simple and moderate.