Sobolev-type error estimates for interpolation by radial basis functions. (English) Zbl 0955.41002

Le Méhauté, Alain (ed.) et al., Surface fitting and multiresolution methods. Vol. 2 of the proceedings of the 3rd international conference on Curves and surfaces, held in Chamonix-Mont-Blanc, France, June 27-July 3, 1996. Nashville, TN: Vanderbilt University Press. 337-344 (1997).
The author derives error estimates for interpolation by radial functions with positive and algebraically decaying Fourier transforms. The resulting Sobolev-type estimates lead to a doubling of the approximation order for certain subspaces of functions. The techniques used are generalizations of methods introduced originally by J. Duchon for thin plate splines [RAIRO, Anal. Numer. 12, 325-334 (1978; Zbl 0403.41003)].
For the entire collection see [Zbl 0927.00040].
Reviewer: E.Quak (Oslo)


41A05 Interpolation in approximation theory
41A30 Approximation by other special function classes


Zbl 0403.41003