The essential rate of approximation for radial function manifold

In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let W p r ( ) be the usual Sobolev class of functions on the unit ball . We study the deviation from the radial function manifolds to W p r ( ). Our results show that the upper and lowe...

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Bibliographic Details
Published in:Science China. Mathematics 2011-09, Vol.54 (9), p.1985-1994
Main Authors: Lin, ShaoBo, Cao, FeiLong, Xu, ZongBen
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let W p r ( ) be the usual Sobolev class of functions on the unit ball . We study the deviation from the radial function manifolds to W p r ( ). Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-011-4262-1