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Computer Science > Mathematical Software
Title: Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy
(Submitted on 21 Mar 2024 (v1), last revised 1 May 2024 (this version, v2))
Abstract: 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 Pad\'{e} 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.
Submission history
From: Jan Verschelde [view email][v1] Thu, 21 Mar 2024 21:28:47 GMT (441kb,D)
[v2] Wed, 1 May 2024 19:04:28 GMT (548kb,D)
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