Multiscale approximation for functions in arbitrary Sobolev spaces by scaled radial basis functions on the unit sphere

In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.

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Bibliographic Details
Published in:Applied and computational harmonic analysis 2012-05, Vol.32 (3), p.401-412
Main Authors: Le Gia, Q.T., Sloan, I.H., Wendland, H.
Format: Article
Language:English
Subjects:
Approximation
Convergence
Fourier analysis
Kernels
Mathematical analysis
Mathematical models
Multiscale approximation
Radial basis function
Sobolev space
Unit sphere
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Description
Summary:In this paper, we prove convergence results for multiscale approximation using compactly supported radial basis functions restricted to the unit sphere, for target functions outside the reproducing kernel Hilbert space of the employed kernel.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2011.07.007