Beyond polyhedral homotopies. (March 2019)

• Record Type: Journal Article
• Authors: Leykin, Anton; Yu, Josephine
• Is Part Of: Journal of symbolic computation. Volume 91(2019)
• Page Start: 173
• Page End: 180
• Publication Date: 2019-03
• Subjects: Numerical algebraic geometry -- Nonlinear algebra -- Tropical geometry -- Homotopy continuation -- Solving polynomial equations; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.019
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present a new algorithmic framework which utilizes tropical geometry and homotopy continuation for solving systems of polynomial equations where some of the polynomials are generic elements in linear subspaces of the polynomial ring. This approach generalizes the polyhedral homotopies by Huber and Sturmfels.