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Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy (2403.14844v2)
Published 21 Mar 2024 in cs.MS, cs.NA, cs.SC, math.CV, and math.NA
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.
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