Resultant-based methods for plane curves intersection problems

Laurent Busé 1 Houssam Khalil 2 Bernard Mourrain 1
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
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.
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Laurent Busé, Houssam Khalil, Bernard Mourrain. Resultant-based methods for plane curves intersection problems. Computer Algebra in Scientific Computing (CASC), Sep 2005, Kalamata, Greece, pp.75-92. ⟨inria-00100288⟩

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