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, Volume 77, Issue 4, pp 387–411 | Cite as

PHoMpara – Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems

  • T. GunjiEmail author
  • S. Kim
  • K. Fujisawa
  • M. Kojima
Article

Abstract

The polyhedral homotopy continuation method is known to be a successful method for finding all isolated solutions of a system of polynomial equations. PHoM, an implementation of the method in C++, finds all isolated solutions of a polynomial system by constructing a family of modified polyhedral homotopy functions, tracing the solution curves of the homotopy equations, and verifying the obtained solutions. A software package PHoMpara parallelizes PHoM to solve a polynomial system of large size. Many characteristics of the polyhedral homotopy continuation method make parallel implementation efficient and provide excellent scalability. Numerical results include some large polynomial systems that had not been solved.

AMS Subject Classifications

65H10 65H20 

Keywords

Polynomials parallel computation homotopy continuation methods equations polyhedral homotopy numerical experiments software package 

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Copyright information

© Springer-Verlag Wien 2006

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of MathematicsEwha Women's UniversitySeoulKorea
  3. 3.Department of Mathematical SciencesTokyo Denki UniversitySaitamaJapan

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