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Parallel Homotopy Algorithms to Solve Polynomial Systems

  • Anton Leykin
  • Jan Verschelde
  • Yan Zhuang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4151)

Abstract

Homotopy continuation methods to compute numerical approximations to all isolated solutions of a polynomial system are known as “embarrassingly parallel”, i.e.: because of their low communication overhead, these methods scale very well for a large number of processors. Because so many important problems remain unsolved mainly due to their intrinsic computational complexity, it would be embarrassing not to develop parallel implementations of polynomial homotopy continuation methods. This paper concerns the development of “parallel PHCpack”, a project which started a couple of years ago in collaboration with Yusong Wang, and which currently continues with Anton Leykin (parallel irreducible decomposition) and Yan Zhuang (parallel polyhedral homotopies). We report on our efforts to make PHCpack ready to solve large polynomial systems which arise in applications.

2000 Mathematics Subject Classification. Primary 65H10. Secondary 14Q99, 68W30.

keywords and phrases

Continuation methods high performance continuation jumpstarting homotopies linear-product systems parallel computation path following polynomial systems polyhedral homotopies simplex system 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Anton Leykin
    • 1
  • Jan Verschelde
    • 1
  • Yan Zhuang
    • 1
  1. 1.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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