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Solving polynomial systems via homotopy continuation and monodromy

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  • Timothy Duff, Georgia Institute of Technology
  • ,
  • Cvetelina Hill, Georgia Institute of Technology
  • ,
  • Anders Jensen
  • Kisun Lee, Georgia Institute of Technology
  • ,
  • Anton Leykin, Georgia Institute of Technology
  • ,
  • Jeff Sommars, University of Illinois at Chicago

We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy-based solvers in terms of decorated graphs. Under the theoretical. that monodromy actions are generated uniformly, we show that the expected number of homotopy paths tracked by an algorithm following this framework is linear in the number of solutions. We demonstrate that our software implementation is competitive with the existing state-of-the-art methods implemented in other software packages.

Original languageEnglish
JournalIMA Journal of Numerical Analysis
Pages (from-to)1421-1446
Number of pages26
Publication statusPublished - Jul 2019

    Research areas

  • homotopy continuation, monodromy, polynomial system solvers, SOLUTION SETS, PROBABILITY

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