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Solving the Birkhoff interpolation problem via the critical point method: an experimental study

Fabrice Rouillier 1, 2 Mohab Safey El Din 2, 1 Eric Schost 3
1 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
2 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 X - École polytechnique
Abstract : Following the work of Gonzalez-Vega, this paper is devoted to show how to use recent algorithmic tools of computational real algebraic geometry to solve the Birkhoff Interpolation Problem. We recall and partly improve two algorithms to find at least one point in each connected component of a real algebraic set defined by a single equation or a polynomial system of equations, both based on the computation of the critical points of a distance function. These algorithms are used to solve the Birkhoff Interpolation Problem in a case which was known to be an open problem.
Mots-clés : infinitésimaux infinitesimals problème d'interpolation de birkhoff birkhoff interpolation problem real solutions singularities solutions réelles singularités
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Conference papers
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https://hal.inria.fr/inria-00099276
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Submitted on : Tuesday, September 26, 2006 - 8:52:21 AM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM

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Fabrice Rouillier, Mohab Safey El Din, Eric Schost. Solving the Birkhoff interpolation problem via the critical point method: an experimental study. Third International Workshop on Automated Deduction in Geometry - ADG'2000, Sep 2000, Zurich, Switzerland. pp.26-40, ⟨10.1007/3-540-45410-1_3⟩. ⟨inria-00099276⟩

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