Structured Backward Error Analysis for Double Saddle Point Problems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908441324290048 |
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| author | Ahmad, Sk. Safique Khatun, Pinki |
| author_facet | Ahmad, Sk. Safique Khatun, Pinki |
| contents | Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore structured BEs for a class of double saddle point problems (DSPPs), aiming to assess the strong backward stability of numerical algorithms devised to find their solution. Our investigations preserve the inherent matrix structure and sparsity pattern in the corresponding perturbation matrices and derive explicit formulae for the structure BEs. Moreover, we provide formulae for the structure-preserving minimal perturbation matrices for which the structured BE is attained. Utilizing the relationship between the DSPP and the least squares problem with equality constraints (LSE), we derive the sparsity-preserving BE formula for LSE within our framework. Numerical experiments are performed to test the strong backward stability of various numerical algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_14019 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structured Backward Error Analysis for Double Saddle Point Problems Ahmad, Sk. Safique Khatun, Pinki Numerical Analysis 15A06, 65F10, 65F99 Backward error (BE) analysis emerges as a powerful tool for assessing the backward stability and strong backward stability of numerical algorithms. In this paper, we explore structured BEs for a class of double saddle point problems (DSPPs), aiming to assess the strong backward stability of numerical algorithms devised to find their solution. Our investigations preserve the inherent matrix structure and sparsity pattern in the corresponding perturbation matrices and derive explicit formulae for the structure BEs. Moreover, we provide formulae for the structure-preserving minimal perturbation matrices for which the structured BE is attained. Utilizing the relationship between the DSPP and the least squares problem with equality constraints (LSE), we derive the sparsity-preserving BE formula for LSE within our framework. Numerical experiments are performed to test the strong backward stability of various numerical algorithms. |
| title | Structured Backward Error Analysis for Double Saddle Point Problems |
| topic | Numerical Analysis 15A06, 65F10, 65F99 |
| url | https://arxiv.org/abs/2408.14019 |