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Yet another eigenvalue algorithm for solving polynomial systems

Numerical Analysis 2022-02-14 v2 Numerical Analysis Symbolic Computation Algebraic Geometry

Abstract

In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions reliably and efficiently. In overdetermined cases, it reduces the task to an eigenvalue problem in a simpler and considerably faster way than in previous methods, and it can outperform the homotopy continuation approach. We provide many examples and an implementation in the proof-of-concept Julia package EigenvalueSolver.jl.

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Cite

@article{arxiv.2105.08472,
  title  = {Yet another eigenvalue algorithm for solving polynomial systems},
  author = {Matías R. Bender and Simon Telen},
  journal= {arXiv preprint arXiv:2105.08472},
  year   = {2022}
}

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30 pages