Factoring solution sets of polynomial systems in parallel
Factoring solution sets of polynomial systems in parallel
复制标题
并行分解多项式系统的解集
DOI：
10.1109/icppw.2005.31
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Verschelde
中科院分区：
文献类型：
--
作者：
A. Leykin;J. Verschelde
报道了多项式系统正维解集因式分解算法的首次并行实现。由于算法采用了同伦延拓，使得路径跟踪作业具有较好的加速比。然而，对于高度的解决方案集，管理不同同伦和大型解决方案列表的开销暴露了主/从并行编程范例对这类问题的限制。一项概率复杂性研究建议对该方法进行修改，这也将改进原始算法的串行版。
The authors reported on a first parallel implementation of a recent algorithm to factor positive dimensional solution sets of polynomial systems. As the algorithm uses homotopy continuation, a good speedup of the path tracking jobs was observed. However, for solution sets of high degree, the overhead of managing different homotopies and large lists of solutions exposes the limits of the master/servant parallel programming paradigm for this type of problem. A probabilistic complexity study suggests modifications to the method, which will also improve the serial version of the original algorithm.