A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation | Zendy

Simon Telen | Zendy; Marc Van Barel | Zendy; Jan Verschelde | Zendy

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A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation

Author(s) -

Simon Telen,

Marc Van Barel,

Jan Verschelde

Publication year - 2020

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/19m1288036

Subject(s) - mathematics , path (computing) , polynomial , algorithm , homotopy , continuation , tracking (education) , homotopy analysis method , numerical continuation , computer science , mathematical analysis , nonlinear system , psychology , pedagogy , pure mathematics , bifurcation , programming language , physics , quantum mechanics

We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision arithmetic. It is based on an adaptive stepsize predictor that uses Pade techniques to detect local difficulties for function approximation and danger for path jumping. We show the potential of the new path tracking algorithm through several numerical examples and compare with existing implementations.

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