Structured Backward Errors of Sparse Generalized Saddle Point Problems with Hermitian Block Matrices
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908434023055360 |
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| author | Ahmad, Sk. Safique Khatun, Pinki |
| author_facet | Ahmad, Sk. Safique Khatun, Pinki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structured Backward Errors of Sparse Generalized Saddle Point Problems with Hermitian Block Matrices Ahmad, Sk. Safique Khatun, Pinki Numerical Analysis 15A12, 65F20, 65F35, 65F99 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. |
| title | Structured Backward Errors of Sparse Generalized Saddle Point Problems with Hermitian Block Matrices |
| topic | Numerical Analysis 15A12, 65F20, 65F35, 65F99 |
| url | https://arxiv.org/abs/2507.03335 |