Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations
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arXiv
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| Autores principales: | , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
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| _version_ | 1866915200765001728 |
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| author | Parkinson, Suzanna Ringer, Hayden Wall, Kate Parkinson, Erik Erekson, Lukas Christensen, Daniel Jarvis, Tyler J. |
| author_facet | Parkinson, Suzanna Ringer, Hayden Wall, Kate Parkinson, Erik Erekson, Lukas Christensen, Daniel Jarvis, Tyler J. |
| contents | We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze performance on one such system in detail, namely the 'devastating example' that Noferini and Townsend used to demonstrate instability of resultant-based methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_03526 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations Parkinson, Suzanna Ringer, Hayden Wall, Kate Parkinson, Erik Erekson, Lukas Christensen, Daniel Jarvis, Tyler J. Numerical Analysis 65H04 We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze performance on one such system in detail, namely the 'devastating example' that Noferini and Townsend used to demonstrate instability of resultant-based methods. |
| title | Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations |
| topic | Numerical Analysis 65H04 |
| url | https://arxiv.org/abs/2104.03526 |