Constructive Approximation

, Volume 5, Issue 1, pp 49–68

Symmetric iterative interpolation processes

  • Gilles Deslauriers
  • Serge Dubuc

DOI: 10.1007/BF01889598

Cite this article as:
Deslauriers, G. & Dubuc, S. Constr. Approx (1989) 5: 49. doi:10.1007/BF01889598


Using a baseb and an even number of knots, we define a symmetric iterative interpolation process. The main properties of this process come from an associated functionF. The basic functional equation forF is thatF(t/b)=σnF(n/b)F(t-n). We prove thatF is a continuous positive definite function. We find almost precisely in which Lipschitz classes derivatives ofF belong. If a functiony is defined only on integers, this process extendsy continuously to the real axis asy(t=∑ny(n)F(tn). Error bounds for this iterative interpolation are given.

AMS classification


Key words and phrases

InterpolationEigenvalueEigenvectorFourier transformLipschitz classesCurve fittingTrigonometric polynomialsRecurrence relationsFactorizationOperators in sequence spaces

Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • Gilles Deslauriers
    • 1
  • Serge Dubuc
    • 2
  1. 1.Département de mathématiques appliquéesÉcole PolytechniqueMontréalCanada
  2. 2.Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada