Error estimates for interpolation by compactly supported radial basis functions of minimal degree. (English) Zbl 0904.41013

The author considers interpolation at \(N\) distinct points \(x_i\in\mathbb{R}^d\), using radial basis functions introduced by him in the paper [Adv. Comput. Math. 4, No. 4, 389-396 (1995; Zbl 0838.41014)]. After identifying the associated Hilbert spaces of these functions as norm-equivalent to certain Sobolev spaces, error estimates for the corresponding interpolants are derived by computing upper and lower bounds for the Fourier transforms of these radial basis functions. Upper bounds for the condition numbers of the interpolation matrices, in terms of the separation distance of the centers \(x_i\), conclude the paper.
Reviewer: E.Quak (Oslo)


41A30 Approximation by other special function classes
41A05 Interpolation in approximation theory
41A63 Multidimensional problems


Zbl 0838.41014
Full Text: DOI


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