Wendland functions with increasing smoothness converge to a Gaussian
Provides a theoretical link between compactly supported radial basis functions and the Gaussian kernel, relevant for approximation theory and kernel methods.
The paper proves that Wendland functions, a class of compactly supported radial basis functions, converge uniformly to a Gaussian as their smoothness parameter increases, with numerical experiments confirming the result.
The Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with a linear change of variables, both the original and the "missing" Wendland functions converge uniformly to a Gaussian as the smoothness parameter approaches infinity. We also give numerical experiments with Wendland functions of different smoothness.