Journal article

Barycentric rational interpolation at quasi-equidistant nodes

  • Hormann, Kai Faculty of Informatics, University of Lugano, Switzerland
  • Klein, Georges Department of Mathematics, University of Fribourg, Switzerland
  • De Marchi, Stefano Department of Pure and Applied Mathematics, University of Padova, Italy
Published in:
  • Dolomites Research Notes on Approximation. - 2012, vol. 5, no. 1, p. 1-6
English A collection of recent papers reveals that linear barycentric rational interpolation with the weights suggested by Floater and Hormann is a good choice for approximating smooth functions, especially when the interpolation nodes are equidistant. In the latter setting, the Lebesgue constant of this rational interpolation process is known to grow only logarithmically with the number of nodes. But since practical applications not always allow to get precisely equidistant samples, we relax this condition in this paper and study the Floater–Hormann family of rational interpolants at distributions of nodes which are only almost equidistant. In particular, we show that the corresponding Lebesgue constants still grow logarithmically, albeit with a larger constant than in the case of equidistant nodes.
Faculté des sciences et de médecine
Département de Mathématiques
  • English
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