PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems The polyhedral homotopy continuation method (PHoM) 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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References in zbMATH (referenced in 4 articles , 1 standard article )
Showing results 1 to 4 of 4.
- Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W.II: Software for numerical algebraic geometry: a paradigm and progress towards its implementation (2008)
- Mizutani, Tomohiko; Takeda, Akiko: DEMiCs: a software package for computing the mixed volume via dynamic enumeration of all mixed cells (2008)
- Gunji, T.; Kim, S.; Fujisawa, K.; Kojima, M.: PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems (2006)
- Leykin, Anton; Verschelde, Jan; Zhuang, Yan: Parallel homotopy algorithms to solve polynomial systems (2006)