Numerische Mathematik

, Volume 121, Issue 3, pp 461-471

First online:

On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

  • Len BosAffiliated withDepartment of Computer Science, University of Verona Email author 
  • , Stefano De MarchiAffiliated withDepartment of Pure and Applied Mathematics, University of Padua
  • , Kai HormannAffiliated withFaculty of Informatics, University of Lugano
  • , Georges KleinAffiliated withDepartment of Mathematics, University of Fribourg

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Recent results reveal that the family of barycentric rational interpolants introduced by Floater and Hormann is very well-suited for the approximation of functions as well as their derivatives, integrals and primitives. Especially in the case of equidistant interpolation nodes, these infinitely smooth interpolants offer a much better choice than their polynomial analogue. A natural and important question concerns the condition of this rational approximation method. In this paper we extend a recent study of the Lebesgue function and constant associated with Berrut’s rational interpolant at equidistant nodes to the family of Floater–Hormann interpolants, which includes the former as a special case.

Mathematics Subject Classification (2000)

65D05 65F35 41A05 41A20