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A Blackbox Polynomial System Solver on Parallel Shared Memory Computers

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Computer Algebra in Scientific Computing (CASC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11077))

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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.

This material is based upon work supported by the National Science Foundation under Grant No. 1440534.

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Correspondence to Jan Verschelde .

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Verschelde, J. (2018). A Blackbox Polynomial System Solver on Parallel Shared Memory Computers. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2018. Lecture Notes in Computer Science(), vol 11077. Springer, Cham. https://doi.org/10.1007/978-3-319-99639-4_25

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  • DOI: https://doi.org/10.1007/978-3-319-99639-4_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99638-7

  • Online ISBN: 978-3-319-99639-4

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