Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909187313762304 |
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| author | Verschelde, Jan Viswanathan, Kylash |
| author_facet | Verschelde, Jan Viswanathan, Kylash |
| contents | PHCpack is a software package for polynomial homotopy continuation, which provides a robust path tracker [Telen, Van Barel, Verschelde, SISC 2020]. This tracker computes the radius of convergence of Newton's method, estimates the distance to the nearest path, and then applies Padé approximants to predict the next point on the path. A priori step size control is less sensitive to finely tuned tolerances than a posteriori step size control, and is therefore robust. The Python interface phcpy is extended with a new step-by-step tracker and is applied to experiment with extrapolation methods to accurately locate the singular points at the end of solution paths. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy Verschelde, Jan Viswanathan, Kylash Mathematical Software Numerical Analysis Symbolic Computation Complex Variables PHCpack is a software package for polynomial homotopy continuation, which provides a robust path tracker [Telen, Van Barel, Verschelde, SISC 2020]. This tracker computes the radius of convergence of Newton's method, estimates the distance to the nearest path, and then applies Padé approximants to predict the next point on the path. A priori step size control is less sensitive to finely tuned tolerances than a posteriori step size control, and is therefore robust. The Python interface phcpy is extended with a new step-by-step tracker and is applied to experiment with extrapolation methods to accurately locate the singular points at the end of solution paths. |
| title | Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy |
| topic | Mathematical Software Numerical Analysis Symbolic Computation Complex Variables |
| url | https://arxiv.org/abs/2403.14844 |