Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy
CoRR(2024)
摘要
A robust path tracker [Telen, Van Barel, Verschelde, SISC 2020] 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. Apriori step size control is less sensitive to finely tuned tolerances
than aposteriori step size control, and is therefore robust. Extrapolation
methods are effective to accurately locate the singular points at the end of
solution paths, as illustrated with phcpy, the scripting interface to PHCpack.
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