The Gibbs Phenomenon for Radial Basis Functions
نویسندگان
چکیده
What is now known as the Gibbs phenomenon was first observed in the context of truncated Fourier expansions, but other versions of it arise also in situations such as truncated integral transforms and for different interpolation methods. Radial basis functions (RBF) is a modern interpolation technique which includes both splines and trigonometric interpolations as special cases in 1-D, and it generalizes these methodologies to scattered node layouts in any number of dimensions. We investigate here the Gibbs phenomenon for 1-D RBF interpolation, and find that it can differ also qualitatively from previously studied cases.
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