Wendland functions with increasing smoothness converge to a Gaussian. (English) Zbl 1298.41002
Summary: 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.
MSC:
| 41A05 | Interpolation in approximation theory |
| 41A15 | Spline approximation |
| 41A30 | Approximation by other special function classes |
| 41A63 | Multidimensional problems |
| 65D07 | Numerical computation using splines |
Software:
MatlabReferences:
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