Article

Computing

, 83:109

First online:

HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method

  • T. L. LeeAffiliated withDepartment of Mathematics, Michigan State University Email author 
  • , T. Y. LiAffiliated withDepartment of Mathematics, Michigan State University
  • , C. H. TsaiAffiliated withDepartment of Mathematics, Michigan State University

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Abstract

HOM4PS-2.0 is a software package in FORTRAN 90 which implements the polyhedral homotopy continuation method for solving polynomial systems. It updates its original version HOM4PS in three key aspects: (1) new method for finding mixed cells, (2) combining the polyhedral and linear homotopies in one step, (3) new way of dealing with curve jumping. Numerical results show that this revision leads to a spectacular speed-up, ranging up to 1950s, over its original version on all benchmark systems, especially for large ones. It surpasses the existing packages in finding isolated zeros, such as PHCpack (Verschelde in ACM Trans Math Softw 25:251–276, 1999), PHoM (Gunji et al. in Computing 73:57–77, 2004), and Bertini (Bates et al. in Software for numerical algebraic geometry. Available at http://​www.​nd.​edu/​~sommese/​bertini), in speed by big margins.

Keywords

Polynomial systems Homotopy continuation methods Polyhedral homotopy Numerical experiments Software package

Mathematics Subject Classification (2000)

65H10 65H15 90B99