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A note on radial basis function interpolant limits. (English) Zbl 1201.65017
The authors study if and when the limits of radial basis functions interpolants with parameters exist. Also, they investigate the dependence of the limit on the properties of the radial functions and on the geometries of the data, and some examples are given.
The authors discover that for some radial basis functions interpolants and some grids one may get divergence. Another phenomenon discovered is that whenever the nodes lie on a circle in the Euclidean plane, numerical tests suggest that the limit always exists and indeed it is the same polynomial for all choices of the radial basis functions.

MSC:
65D05 Numerical interpolation
41A05 Interpolation in approximation theory
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