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Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods

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Frontiers of Combining Systems (FroCoS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2309))

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Abstract

The solving engines of most of constraint programming systems use interval-based consistency techniques to process nonlinear systems over the reals. However, few symbolic-interval cooperative solvers are implemented. The challenge is twofold: control of the amount of symbolic computations, and prediction of the accuracy of interval computations over transformed systems.

In this paper, we introduce a new symbolic pre-processing for interval branch-and-prune algorithms based on box consistency. The symbolic algorithm computes a linear relaxation by abstraction of the nonlinear terms. The resulting rectangular linear system is processed by Gaussian elimination. Control strategies of the densification of systems during elimination are devised. Three scalable problems known to be hard for box consistency are efficiently solved.

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Author information

Authors and Affiliations

  1. IRIN - University of Nantes, 2, rue de la Houssinière, 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. DIST, Università di Genova, Viale Causa 13, 15145, Genova, Italy

    Alessandro Armando

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© 2002 Springer-Verlag Berlin Heidelberg

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Ceberio, M., Granvilliers, L. (2002). Solving Nonlinear Equations by Abstraction, Gaussian Elimination, and Interval Methods. In: Armando, A. (eds) Frontiers of Combining Systems. FroCoS 2002. Lecture Notes in Computer Science(), vol 2309. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45988-X_10

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  • DOI: https://doi.org/10.1007/3-540-45988-X_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43381-1

  • Online ISBN: 978-3-540-45988-0

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