Extrapolating on Taylor Series Solutions of Homotopies with Nearby Poles
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913333189279744 |
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| author | Verschelde, Jan Viswanathan, Kylash |
| author_facet | Verschelde, Jan Viswanathan, Kylash |
| contents | A polynomial homotopy is a family of polynomial systems in one parameter, which defines solution paths starting from known solutions and ending at solutions of a system that has to be solved. We consider paths leading to isolated singular solutions, to which the Taylor series converges logarithmically. Whether or not extrapolation algorithms manage to accelerate the slowly converging series depends on the proximity of poles close to the disk of convergence of the Taylor series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extrapolating on Taylor Series Solutions of Homotopies with Nearby Poles Verschelde, Jan Viswanathan, Kylash Numerical Analysis A polynomial homotopy is a family of polynomial systems in one parameter, which defines solution paths starting from known solutions and ending at solutions of a system that has to be solved. We consider paths leading to isolated singular solutions, to which the Taylor series converges logarithmically. Whether or not extrapolation algorithms manage to accelerate the slowly converging series depends on the proximity of poles close to the disk of convergence of the Taylor series. |
| title | Extrapolating on Taylor Series Solutions of Homotopies with Nearby Poles |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.17681 |