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Error estimates for interpolation by compactly supported radial basis functions of minimal degree
journal contribution
posted on 2023-06-07, 22:10 authored by Holger WendlandWe consider error estimates for interpolation by a special class of compactly supported radial basis functions. These functions consist of a univariate polynomial within their support and are of minimal degree depending on space dimension and smoothness. Their associated “native” Hilbert spaces are shown to be norm-equivalent to Sobolev spaces. Thus we can derive approximation orders for functions from Sobolev spaces which are comparable to those of thin-plate-spline interpolation. Finally, we investigate the numerical stability of the interpolation process.
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Publication status
- Published
Journal
Journal of Approximation TheoryISSN
0021-9045Publisher
ElsevierExternal DOI
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2Volume
93Page range
258-272Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2012-02-06Usage metrics
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