Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations
Numerical Analysis
2025-03-18 v1 Numerical Analysis
Abstract
We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze performance on one such system in detail, namely the 'devastating example' that Noferini and Townsend used to demonstrate instability of resultant-based methods.
Cite
@article{arxiv.2104.03526,
title = {Analysis of Normal-Form Algorithms for Solving Systems of Polynomial Equations},
author = {Suzanna Parkinson and Hayden Ringer and Kate Wall and Erik Parkinson and Lukas Erekson and Daniel Christensen and Tyler J. Jarvis},
journal= {arXiv preprint arXiv:2104.03526},
year = {2025}
}
Comments
Associated code available at https://github.com/tylerjarvis/eigen_rootfinding