Structured backward errors for block three-by-three saddle point systems with Hermitian and sparsity block matrices
Year: 2025
Type: article
Abstract: In this paper, we explore the structured backward errors for a class of block three-by-three saddle point systems with Hermitian and sparsity block matrices. We derive an explicit formula for the structured backward errors under the assumption that the inherent matrix structure and sparsity pattern are maintained in the associated perturbation. Moreover, the optimal backward perturbation matrix for achieving structured backward error is constructed. Our analysis further explores the structured backward error when the sparsity structure is not preserved. Numerical experiments show that the computable formulas of structured backward errors are useful for testing the stability of practical algorithms.
Source: Results in Applied Mathematics
Authors: Bing Tan, Wei Ma
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,770
OpenAlex ID: W4407884396