Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy
<|reference_start|>Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy: 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.<|reference_end|>
@article{verschelde2024extrapolating,
    title={Extrapolating Solution Paths of Polynomial Homotopies towards
  Singularities with PHCpack and phcpy},
    author={Jan Verschelde and Kylash Viswanathan},
    journal={arXiv preprint arXiv:2403.14844},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.14844},
    primaryClass={cs.MS cs.NA cs.SC math.CV math.NA}
}