Locality properties of radial basis function expansion coefficients for equispaced interpolation

AMS Citation:
Fornberg, B., N. Flyer, S. Hovde, and C. Piret, 2008: Locality properties of radial basis function expansion coefficients for equispaced interpolation. IMA Journal of Numerical Analysis, 28, 121-142, doi:10.1093/imanum/drm014.
Date:2008-01-01
Resource Type:article
Title:Locality properties of radial basis function expansion coefficients for equispaced interpolation
Abstract: Many types of radial basis functions (RBFs) are global in terms of having large magnitude across the entire domain. Yet, in contrast, e.g. with expansions in orthogonal polynomials, RBF expansions exhibit a strong property of locality with regard to their coefficients. That is, changing a single data value mainly affects the coefficients of the RBFs which are centred in the immediate vicinity of that data location. This locality feature can be advantageous in the development of fast and well-conditioned iterative RBF algorithms. With this motivation, we employ here both analytical and numerical techniques to derive the decay rates of the expansion coefficients for cardinal data, in both 1D and 2D. Furthermore, we explore how these rates vary in the interesting high-accuracy limit of increasingly flat RBFs.
Subject(s):Radial basis functions, RBF, Cardinal interpolation
Peer Review:Refereed
Copyright Information:An edited version of this paper was published by the IMA. Copyright 2008 IMA.
OpenSky citable URL: ark:/85065/d7p84c1m
Publisher's Version: 10.1093/imanum/drm014
Author(s):
  • Bengt Fornberg
  • Natasha Flyer - NCAR/UCAR
  • Susan Hovde
  • Cécile Piret
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