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

  • Fabrice Rouillier
  • Mohab Safey El Din
  • Éric Schost
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2061)


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.:


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Fabrice Rouillier
    • 1
  • Mohab Safey El Din
    • 2
  • Éric Schost
    • 3
  1. 1.LORIAINRIA-LorraineNancyFrance
  2. 2.CALFOR, LIP6Université Paris VIParisFrance
  3. 3.Laboratoire GAGEÉcole PolytechniquePalaiseauFrance

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