Volume 63, pp. 401-423, 2025.

Structured backward errors of sparse generalized saddle point problems with Hermitian block matrices

Sk. Safique Ahmad and Pinki Khatun

Abstract

In this paper, we derive the structured backward error (BE) for a class of generalized saddle point problems (GSPPs) with perturbations preserving the sparsity pattern and the Hermitian structures of the block matrices. Additionally, we construct the optimal backward perturbation matrices for which the structured BE is achieved. Our analysis also examines the structured BE in cases where the sparsity pattern is not maintained. Through numerical experiments, we demonstrate the reliability of the obtained structured BEs and the corresponding optimal backward perturbations. Finally, the computed structured BEs are used to assess the strong backward stability of some numerical methods used to solve the GSPP.

Full Text (PDF) [397 KB], BibTeX , DOI: 10.1553/etna_vol63s401

Key words

Hermitian matrices, backward error, perturbation analysis, saddle point problems, sparsity

AMS subject classifications

15A12, 65F20, 65F35, 65F99

Links to the cited ETNA articles

[3]	Vol. 60 (2024), pp. 471-500 Sk. Safique Ahmad and Pinki Khatun: Structured condition numbers for a linear function of the solution of the generalized saddle point problem