A Blackbox Polynomial System Solver on Parallel Shared Memory Computers

2018/04/11 by Verschelde, Jan
#Algebraic Geometry (math.AG) #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Parallel #Symbolic Computation (cs.SC) #and Cluster Computing (cs.DC)

paper · doi:10.48550/arxiv.1804.03807

Abstract

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.

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