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On the efficiency of interpolation by radial basis functions. (English) Zbl 0937.65013
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. 309-318 (1997).
Summary: We study the computational complexity, the error behavior, and the numerical stability of interpolation by radial basis functions. It turns out that these issues are intimately connected. For the case of compactly supported radial basis functions, we consider the possibility of getting reasonably good reconstructions of $$d$$-variate functions from $$N$$ data at $${\mathcal O}(Nd)$$ computational cost and give some supporting theoretical results and numerical examples.
For the entire collection see [Zbl 0927.00040].

##### MSC:
 65D05 Numerical interpolation 65Y20 Complexity and performance of numerical algorithms