PHoMpara - Parallel implementation of the polyhedral homotopy continuation method for polynomial systems

T. Gunji, S. Kim, Katsuki Fujisawa, M. Kojima

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)387-411
Number of pages25
JournalComputing (Vienna/New York)
Volume77
Issue number4
DOIs
Publication statusPublished - Jun 1 2006

Fingerprint

Homotopy Continuation Method
Polynomial Systems
Parallel Implementation
Polynomials
Homotopy
Polynomial equation
Tracing
C++
Software Package
Scalability
Software packages
Numerical Results
Curve

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

PHoMpara - Parallel implementation of the polyhedral homotopy continuation method for polynomial systems. / Gunji, T.; Kim, S.; Fujisawa, Katsuki; Kojima, M.

In: Computing (Vienna/New York), Vol. 77, No. 4, 01.06.2006, p. 387-411.

Research output: Contribution to journalArticle

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