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Hermite-Birkhoff interpolation of scatterd data by radial basis functions. (English) Zbl 0757.41009
Summary: For Hermite-Birkhoff interpolation of scattered multidimensional data by the radial basis function \(\varphi\), existence and characterization theorems and a variational principle are proved. Examples include \(\varphi(r)=r^ b\), Duchon’s thin-plate splines, Hardy’s multiquadrics, and inverse multiquadrics.

MSC:
41A05 Interpolation in approximation theory
41A15 Spline approximation
41A30 Approximation by other special function classes
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