Solving polynomial systems via homotopy continuation and monodromy

Timothy Duff, Cvetelina Hill, Anders Jensen, Kisun Lee, Anton Leykin*, Jeff Sommars

*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

Abstract

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.

OriginalsprogEngelsk
TidsskriftIMA Journal of Numerical Analysis
Vol/bind39
Nummer3
Sider (fra-til)1421-1446
Antal sider26
ISSN0272-4979
DOI
StatusUdgivet - jul. 2019

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