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Resultant-Based Methods for Plane Curves Intersection Problems

  • Laurent Busé
  • Houssam Khalil
  • Bernard Mourrain
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3718)

Abstract

We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations.

Keywords

Intersection Point Singular Value Decomposition Polynomial System Multiple Root Quotient Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Laurent Busé
    • 1
  • Houssam Khalil
    • 2
  • Bernard Mourrain
    • 1
  1. 1.INRIA, GalaadSophia AntipolisFrance
  2. 2.Laboratoire de Mathématiques Appliquées de LyonUCBL and CNRSVilleurbanneFrance

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