Numerische Mathematik

, Volume 138, Issue 3, pp 615–633 | Cite as

On rational functions without Froissart doublets

  • Bernhard Beckermann
  • George Labahn
  • Ana C. Matos


In this paper we consider the problem of working with rational functions in a numeric environment. A particular problem when modeling with such functions is the existence of Froissart doublets, where a zero is close to a pole. We discuss three different parameters which allow one to monitor the absence of Froissart doublets for a given general rational function. These include the euclidean condition number of an underlying Sylvester-type matrix, a parameter for determining coprimeness of two numerical polynomials and bounds on the spherical derivative. We show that our parameters sharpen those found in a previous paper by two of the authors.

Mathematics Subject Classification

41A21 65F22 


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  • Bernhard Beckermann
    • 1
  • George Labahn
    • 2
  • Ana C. Matos
    • 1
  1. 1.Laboratoire Painlevé UMR 8524, UFR Mathématiques – M3Université de LilleVilleneuve d’Ascq CedexFrance
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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