A Perturbation Method for Index Detection for Linear Matrix Pencils
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915883139465216 |
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| author | Blazhko, Hanna Wojtylak, Michał |
| author_facet | Blazhko, Hanna Wojtylak, Michał |
| contents | Rigorous, non-asymptotic bounds for the Puiseux expansion of the eigenvalue at infinity are given. Error analysis is provided. Further, the expected value of the eigenvector condition number of a randomly perturbed matrix is estimated. The latter result is applied to the Cayley transform of the linear pencil. Numerical simulations illustrating the theoretical findings are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21771 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Perturbation Method for Index Detection for Linear Matrix Pencils Blazhko, Hanna Wojtylak, Michał Numerical Analysis Rigorous, non-asymptotic bounds for the Puiseux expansion of the eigenvalue at infinity are given. Error analysis is provided. Further, the expected value of the eigenvector condition number of a randomly perturbed matrix is estimated. The latter result is applied to the Cayley transform of the linear pencil. Numerical simulations illustrating the theoretical findings are provided. |
| title | A Perturbation Method for Index Detection for Linear Matrix Pencils |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.21771 |