Error estimates for interpolation by compactly supported radial basis functions of minimal degree
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.
scientific article; zbMATH DE number 1197081
scientific article