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October 20, 2025Open Access

Structured Backward Errors of Sparse Generalized Saddle Point Problems with Hermitian Block Matrices

Key Points

The structured backward error is derived while preserving the sparsity and Hermitian structure of matrices.
Optimal backward perturbation matrices are constructed, achieving the structured backward error effectively.
Numerical experiments validate the reliability of structured backward errors and optimal perturbations in various cases.
The analysis assesses strong backward stability of numerical methods applied to generalized saddle point problems.

Abstract

In this paper, we derive the structured backward error (BE) for a class of generalized saddle point problems (GSPP) by preserving the sparsity pattern and 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 derived structured BEs and the corresponding optimal backward perturbations. Additionally, the derived structured BEs are used to assess the strong backward stability of numerical methods for solving the GSPP.

Structured Backward Errors of Sparse Generalized Saddle Point Problems with Hermitian Block Matrices

Key Points

Abstract

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