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arXiv · 1805.12212

Monodromy Solver: Sequential and Parallel

Nathan Bliss·Timothy Duff·Anton Leykin·Jeff Sommars
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Abstract

We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows a framework developed in previous work and can operate in the presence of a large number of failures of the homotopy continuation subroutine. We give special attention to parallelization and probabilistic analysis of a model adapted to parallelization and failures. Apart from theoretical results, we developed a simulator that allows us to run a large number of experiments without recomputing the outcomes of the continuation subroutine.

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Nathan Bliss, Timothy Duff, Anton Leykin, Jeff Sommars. 2018-05-30. Monodromy Solver: Sequential and Parallel. https://arxiv.org/abs/1805.12212

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