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Solving polynomial systems via homotopy continuation and monodromy

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DOI

  • Timothy Duff, Georgia Inst Technol, University System of Georgia, Georgia Institute of Technology, Dept Math
  • ,
  • Cvetelina Hill, Georgia Inst Technol, University System of Georgia, Georgia Institute of Technology, Dept Math
  • ,
  • Anders Jensen
  • Kisun Lee, Georgia Inst Technol, University System of Georgia, Georgia Institute of Technology, Dept Math
  • ,
  • Anton Leykin, Georgia Inst Technol, University System of Georgia, Georgia Institute of Technology, Dept Math
  • ,
  • Jeff Sommars, Univ Illinois, University of Illinois System, University of Illinois Chicago, University of Illinois Chicago Hospital, Dept Math Stat & Comp Sci

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
Volume39
Issue3
Pages (from-to)1421-1446
Number of pages26
ISSN0272-4979
DOIs
Publication statusPublished - Jul 2019

    Research areas

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

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