PHoMpara – Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems
PHoMpara – Parallel Implementation of the Polyhedral Homotopy Continuation Method for Polynomial Systems
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PHoMpara – 多项式系统多面同伦延拓方法的并行实现
DOI：
10.1007/s00607-006-0166-2
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发表时间：
2006
期刊：
影响因子：
3.7
通讯作者：
M. Kojima
中科院分区：
文献类型：
--
作者：
Takayuki Gunji;Sunyoung Kim;K. Fujisawa;M. Kojima
众所周知，多面体同伦连续方法是寻找多项式方程组的所有孤立解的成功方法。 PHoM 是该方法在 C++ 中的实现，通过构造一系列修改的多面同伦函数、追踪同伦方程的解曲线并验证所获得的解，找到多项式系统的所有孤立解。软件包 PHoMpara 并行化 PHoM 来求解大型多项式系统。多面体同伦延拓方法的许多特性使得并行实现高效并提供出色的可扩展性。数值结果包括一些尚未求解的大型多项式系统。
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.