Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study

Authors:
Fabrice Rouillier;Mohab Safey El Din;Éric Schost
Affiliations:
-;-;-
Venue:
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
Year:
2000

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ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry

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Abstract

Following the work of Gonzalez-Vega, this paper is devoted to showing 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 system of polynomial 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 as an open problem. The solution is available at the U.R.L.: http://www-calfor.lip6.fr/~safey/applications.html.