A Blackbox Polynomial System Solver on Parallel Shared Memory Computers
A Blackbox Polynomial System Solver on Parallel Shared Memory Computers
复制标题
并行共享内存计算机上的黑盒多项式系统求解器
DOI：
10.1007/978-3-319-99639-4_25
复制
发表时间：
2018
影响因子：
2.1
通讯作者：
J. Verschelde
中科院分区：
文献类型：
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作者：
J. Verschelde
多项式系统的数值不可约分解提供了系统的所有正维解集的不可约因子的表示，从它的孤立解中分离出来。应用同伦延拓方法计算一个数值不可约分解。负载平衡和流水线是在多核处理器计算机上并行实现的技术。说明了并行算法在求解循环$n$根问题上的应用，特别是求解$n = 8,9 $和~12的问题。
A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods are applied to compute a numerical irreducible decomposition. Load balancing and pipelining are techniques in a parallel implementation on a computer with multicore processors. The application of the parallel algorithms is illustrated on solving the cyclic $n$-roots problems, in particular for $n = 8, 9$, and~12.