A Blackbox Polynomial System Solver on Parallel Shared Memory Computers

04/11/2018

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by   Jan Verschelde, et al.

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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.