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A Blackbox Polynomial System Solver on Parallel Shared Memory Computers

  • Jan VerscheldeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11077)

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.

Keywords

Homotopy continuation Numerical irreducible decomposition Mathematical software Multitasking Pipelining Polyhedral homotopies Polynomial system Shared memory parallel computing 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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