Mixed cell computation in Hom4PS-3

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• 作者：Tianran Chen^a ; ¹ ; ^{chentia1@msu.edu" class="auth_mail" title="E-mail the corresponding author} ; Tsung-Lin Lee^b ; ² ; ^{leetsung@math.nsysu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Tien-Yien Li^a ; ¹ ; ³ ; ^{li@math.msu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Mixed volume ; Mixed cells ; Polyhedral homotopy ; Polynomial system ; Parallel computing
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P3
• 页码：516-534
• 全文大小：685 K

文摘

This article presents recent efforts in improving the efficiency and scalability of the mixed cell computation step in the context of the Polyhedral Homotopy method.

Solving systems of polynomial equations is an important problem in applied mathematics. The Polyhedral Homotopy method is an important numerical method for this task. In this method, a necessary preprocessing step, known as the “mixed cell computation” problem has been the main bottleneck in the parallel efficiency and scalability. This article presents recent remarkable improvements in the parallel scalability of the algorithm that are applicable to a wide range of hardware architectures including multi-core systems, NUMA systems, computer clusters, and GPUs devices.