Polynomial Homotopies for Dense, Sparse and Determinantal Systems
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Algebraic Geometry
Abstract
Numerical homotopy continuation methods for three classes of polynomial systems are presented. For a generic instance of the class, every path leads to a solution and the homotopy is optimal. The counting of the roots mirrors the resolution of a generic system that is used to start up the deformations. Software and applications are discussed.
Cite
@article{arxiv.math/9907060,
title = {Polynomial Homotopies for Dense, Sparse and Determinantal Systems},
author = {Jan Verschelde},
journal= {arXiv preprint arXiv:math/9907060},
year = {2025}
}