Solving polynomial systems via homotopy continuation and monodromy. (13th April 2018)

• Record Type: Journal Article
• Authors: Duff, Timothy; Hill, Cvetelina; Jensen, Anders; Lee, Kisun; Leykin, Anton; Sommars, Jeff
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 3(2019)
• Page Start: 1421
• Page End: 1446
• Publication Date: 2018-04-13
• Subjects: homotopy continuation -- monodromy -- polynomial system solvers; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry017
• Languages: English
• ISSNs: 0272-4979

Abstract

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.