PHoM - a polyhedral homotopy continuation method for polynomial systems
PHoM - a polyhedral homotopy continuation method for polynomial systems
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DOI：
10.1007/s00607-003-0032-4
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发表时间：
2004-07-01
期刊：
影响因子：
3.7
通讯作者：
Mizutani, T
中科院分区：
文献类型：
--
作者：
Gunji, T;Kim, S;Mizutani, T
PHIM是一个用C++语言编写的软件包，用于使用多面体同伦连续法寻找多项式系统的所有孤立解。在构成包的三个模块中，第一个模块StartSystem基于多面体同伦理论，从给定的多项式方程组f(X)=0的输入数据构造多面体-线性同伦函数族。第二个模块CMPSc跟踪同伦方程的解曲线，以计算f(X)=0的所有孤立解。第三个模块VERIFY检查是否已经正确地逼近了f(X)=0的所有孤立解。我们描述了每个模块中使用的数值方法以及该程序包的用法。数值结果证明了PHOM的性能，包括一些以前没有求解过的大型多项式系统。
PHoM is a software package in C++ for finding all isolated solutions of polynomial systems using a polyhedral homotopy continuation method. Among three modules constituting the package, the first module StartSystem constructs a family of polyhedral-linear homotopy functions, based on the polyhedral homotopy theory, from input data for a given system of polynomial equations f(x)=0. The second module CMPSc traces the solution curves of the homotopy equations to compute all isolated solutions of f(x)=0. The third module Verify checks whether all isolated solutions of f(x)=0 have been approximated correctly. We describe numerical methods used in each module and the usage of the package. Numerical results to demonstrate the performance of PHoM include some large polynomial systems that have not been solved previously.