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Numerical Local Irreducible Decomposition

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

Abstract

Globally, the solution set of a system of polynomial equations with complex coefficients can be decomposed into irreducible components. Using numerical algebraic geometry, each irreducible component is represented using a witness set thereby yielding a numerical irreducible decomposition of the solution set. Locally, the irreducible decomposition can be refined to produce a local irreducible decomposition. We define local witness sets and describe a numerical algebraic geometric approach for computing a numerical local irreducible decomposition for polynomial systems. Several examples are presented.

D.A. Brake—Supported in part by supported in part by NSF ACI-1460032.

J.D. Hauenstein—Supported in part by Army Young Investigator Program (YIP), a Sloan Research Fellowship, and NSF ACI-1460032.

A.J. Sommese—Supported in part by the Vincent J. and Annamarie Micus Duncan Chair of Mathematics and NSF ACI-1440607.

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Authors and Affiliations

  1. Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Daniel A. Brake, Jonathan D. Hauenstein & Andrew J. Sommese

Authors
  1. Daniel A. Brake
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  2. Jonathan D. Hauenstein
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  3. Andrew J. Sommese
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Corresponding author

Correspondence to Daniel A. Brake .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Brake, D.A., Hauenstein, J.D., Sommese, A.J. (2016). Numerical Local Irreducible Decomposition. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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