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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
##### Keywords:
Hermite-Birkhoff interpolation; radial basis function