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

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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.

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo, 152-8552, Japan

    T. Gunji & M. Kojima

  2. Department of Mathematics, Ewha Women's University, 11-1 Dahyun-dong, Sudaemoon-gu, Seoul, 120-750, Korea

    S. Kim

  3. Department of Mathematical Sciences, Tokyo Denki University, Ishizuka, Hatoyama, Saitama, 350-0394, Japan

    K. Fujisawa

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  1. T. Gunji
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  2. S. Kim
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  3. K. Fujisawa
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  4. M. Kojima
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Correspondence to T. Gunji.

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Gunji, T., Kim, S., Fujisawa, K. et al. PHoMpara – Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems. Computing 77, 387–411 (2006). https://doi.org/10.1007/s00607-006-0166-2

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  • DOI: https://doi.org/10.1007/s00607-006-0166-2

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