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Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic

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Artificial Intelligence and Symbolic Computation (AISC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1930))

Abstract

A reliable symbolic-numeric algorithm for solving nonlinear systems over the reals is designed. The symbolic step generates a new system, where the formulas are different but the solutions are preserved, through partial factorizations of polynomial expressions and constraint inversion. The numeric step is a branch-and-prune algorithm based on interval constraint propagation to compute a set of outer approximations of the solutions. The processing of the inverted constraints by interval arithmetic provides a fast and efficient method to contract the variables' domains. A set of experiments for comparing several constraint solvers is reported.

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Author information

Authors and Affiliations

  1. IRIN, Université de Nantes, B.P. 92208, F-44322, Nantes Cedex 3, France

    Martine Ceberio & Laurent Granvilliers

Authors
  1. Martine Ceberio
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  2. Laurent Granvilliers
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Editor information

Editors and Affiliations

  1. University College London, Gower Street, WC1E 6BT, London, UK

    John A. Campbell

  2. Dept. Algebra, Fac. Educación, Universidad Complutense de Madrid, c/Rector Royo Villanova s/n, 28040, Madrid, Spain

    Eugenio Roanes-Lozano

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© 2001 Springer-Verlag Berlin Heidelberg

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Ceberio, M., Granvilliers, L. (2001). Solving Nonlinear Systems by Constraint Inversion and Interval Arithmetic. In: Campbell, J.A., Roanes-Lozano, E. (eds) Artificial Intelligence and Symbolic Computation. AISC 2000. Lecture Notes in Computer Science(), vol 1930. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44990-6_10

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  • DOI: https://doi.org/10.1007/3-540-44990-6_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42071-2

  • Online ISBN: 978-3-540-44990-4

  • eBook Packages: Springer Book Archive

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