Abstract
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.
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Communicated by: Robert Schaback
This work was supported by the Australian Research Council. The authors thank Holger Wendland, Robert Schaback and Simon Hubbert for helpful discussions
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Chernih, A., Sloan, I.H. & Womersley, R.S. Wendland functions with increasing smoothness converge to a Gaussian. Adv Comput Math 40, 185–200 (2014). https://doi.org/10.1007/s10444-013-9304-5
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DOI: https://doi.org/10.1007/s10444-013-9304-5