STRUCTURED BACKWARD ERRORS OF SPARSE GENERALIZED SADDLE POINT PROBLEMS WITH HERMITIAN BLOCK MATRICES

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. © 2025 Elsevier B.V., All rights reserved.