Error estimates for interpolation by compactly supported radial basis functions of minimal degree
type: Item
instance of: scholarly article
title: Error estimates for interpolation by compactly supported radial basis functions of minimal degree
zbMATH Open document ID: 0904.41013
author: Holger Wendland
published in: Journal of Approximation Theory
publication date: 1999-01-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 1197081
zbMATH Keywords: error estimates
zbMATH Keywords: condition numbers
zbMATH Keywords: radial basis functions
zbMATH Keywords: interpolation
reviewed by: E. Quak
MaRDI profile type: Publication
full work available at URL: jath.1997.3137
OpenAlex ID: W2021969763
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DOI: 10.1006/JATH.1997.3137
description: scientific article; zbMATH DE number 1197081