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Some observations regarding interpolants in the limit of flat radial basis functions. (English) Zbl 1048.41017
The authors study here multivariate interpolants based on Radial Basis Functions (RBF) featuring a shape parameter $$\epsilon$$. This study discusses theoretical and computational aspects as the $$\epsilon \rightarrow 0$$ limit. It is conjectured that the Gaussian (GA) RBF interpolants will never diverge as $$\epsilon\to 0$$. Strong evidence in support of this conjecture is given through various experiments with a numerical algorithm also described in the paper (cf. a forthcoming paper by B. Fornberg and G. Wright which is to appear in Comput. Math. Appl.).

MSC:
 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 41A30 Approximation by other special function classes
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