Multiplicative perturbation bounds for the Generalized block Cholesky downdating problem

TL;DR

This paper derives explicit multiplicative perturbation bounds for the Generalized block Cholesky downdating problem using advanced mathematical techniques, providing both strong and weak bounds with numerical validation.

Contribution

It introduces new rigorous multiplicative perturbation bounds for the problem, combining matrix-vector equations, Lyapunov functions, and fixed point theorems.

Findings

Explicit strong and weak multiplicative bounds derived

Numerical experiments validate the theoretical results

Enhanced understanding of perturbation effects in Cholesky downdating

Abstract

The explicit expressions for the strong and the weak rigorous multiplicative perturbation bounds for the Generalized block Cholesky downdating problem are obtained. By bringing together the modified matrix-vector equation approach with the method of Lyapunov majorant function and the Banach fixed point theorem, we derived the strong rigorous multiplicative perturbation bounds. By using the matrix-equation approach the weak rigorous multiplicative bounds are presented. Numerical experiments are provided to illustrate the obtained results.