Stability of kernel-based interpolation
type: Item
instance of: scholarly article
title: Stability of kernel-based interpolation
zbMATH Open document ID: 1188.41001
author: Robert Schaback
author: Stefano De Marchi
published in: Advances in Computational Mathematics
publication date: 2010-02-25T00:00:00Z
review text: For radial basis and other kernel functions, the stability of the interpolation problem with respect to the approximation space is studied. That is, no particular bases are prescribed, but the ability of the spaces to provide stable approximations is considered. While first choices for the bases such as the kernels themselves often provide bad results, as has been noted in early applications, it is shown in this paper that this is not a property of the space which can do better. The kernels which are addressed do not include the infinitely smooth ones, such as multiquadrics, where the situation is still worse than in the kernels of limited differentiability. The importance of this approach comes from the popularity of the radial basis function interpolation method and its implementation.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 5675106
zbMATH Keywords: kernel-based interpolation
zbMATH Keywords: numerical stability
zbMATH Keywords: Lebesgue constants
MaRDI profile type: Publication
full work available at URL: s10444-008-9093-4
OpenAlex ID: W2102551828
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DOI: 10.1007/S10444-008-9093-4
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description: scientific article; zbMATH DE number 5675106