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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.21101 |
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| _version_ | 1866916970115366912 |
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| author | Kalita, Ritwik Prabin Prajapati, Anshul Sharma, Punit |
| author_facet | Kalita, Ritwik Prabin Prajapati, Anshul Sharma, Punit |
| contents | We derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations. We obtain an exact expression for the structured condition number of simple eigenvalues of symmetric, skew-symmetric and even/odd rational matrix functions, and tight bounds are obtained for simple eigenvalues of Hermitian, skew-Hermitian, even/odd, and palindromic rational matrix functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On structured condition number of rational matrix functions Kalita, Ritwik Prabin Prajapati, Anshul Sharma, Punit Optimization and Control We derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations. We obtain an exact expression for the structured condition number of simple eigenvalues of symmetric, skew-symmetric and even/odd rational matrix functions, and tight bounds are obtained for simple eigenvalues of Hermitian, skew-Hermitian, even/odd, and palindromic rational matrix functions. |
| title | On structured condition number of rational matrix functions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.21101 |