Numerische Mathematik

, Volume 121, Issue 3, pp 461–471

On the Lebesgue constant of barycentric rational interpolation at equidistant nodes

  • Len Bos
  • Stefano De Marchi
  • Kai Hormann
  • Georges Klein
Article

DOI: 10.1007/s00211-011-0442-8

Cite this article as:
Bos, L., De Marchi, S., Hormann, K. et al. Numer. Math. (2012) 121: 461. doi:10.1007/s00211-011-0442-8

Abstract

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)

65D0565F3541A0541A20

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Len Bos
    • 1
  • Stefano De Marchi
    • 2
  • Kai Hormann
    • 3
  • Georges Klein
    • 4
  1. 1.Department of Computer ScienceUniversity of VeronaVeronaItaly
  2. 2.Department of Pure and Applied MathematicsUniversity of PaduaPaduaItaly
  3. 3.Faculty of InformaticsUniversity of LuganoLuganoSwitzerland
  4. 4.Department of MathematicsUniversity of FribourgFribourgSwitzerland