On lower bounds in radial basis approximation
type: Item
instance of: scholarly article
title: On lower bounds in radial basis approximation
zbMATH Open document ID: 1064.41008
published in: Advances in Computational Mathematics
publication date: 2005-03-04T00:00:00Z
review text: In this paper, upper bounds on the obtainable approximation orders of radial basis function approximations to approximands from Sobolev spaces are established. For this, any radial basis function of the thin-plate spline type is considered as in earlier papers, especially by Johnson, but the results are improved. For instance, for certain choices of the Sobolev spaces (namely, \(W^k_\infty\)) and the uniform norm for the error estimate, exact orders for the approximation are shown by combining the new lower bounds on the error (i.e., upper bounds on the order of the error) with the known upper bounds on the error (i.e., lower bounds on its order). The centres by which the radial basis functions are shifted when these approximations are applied, are allowed to be scattered.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 2140536
zbMATH Keywords: approximation order
zbMATH Keywords: radial basis function
zbMATH Keywords: Sobolev space
author: Vitaly Maiorov
MaRDI profile type: Publication
full work available at URL: s10444-004-1090-7
OpenAlex ID: W2025185420
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DOI: 10.1007/S10444-004-1090-7
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description: scientific article; zbMATH DE number 2140536