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A Blackbox Polynomial System Solver on Parallel Shared Memory Computers (1804.03807v2)
Published 11 Apr 2018 in cs.MS, cs.DC, cs.SC, math.AG, and math.NA
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.