Advances in Computational Mathematics

, Volume 40, Issue 1, pp 185–200 | Cite as

Wendland functions with increasing smoothness converge to a Gaussian

  • A. Chernih
  • I. H. Sloan
  • R. S. Womersley


The Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with an appropriate rescaling of the variables, both the original and the “missing” Wendland functions converge uniformly to a Gaussian as the smoothness parameter approaches infinity. We also explore the convergence numerically with Wendland functions of different smoothness.


Radial basis functions Compact support Smoothness Wendland functions Gaussian 

Mathematics Subject Classification (2010)

33C90 41A05 41A15 41A30 41A63 65D07 65D10 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of New South WalesSydneyAustralia

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