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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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