Article

The Convergence Rate for a K-Functional in Learning Theory

Journal of Inequalities and Applications 01/2010; DOI:http://www.doaj.org/doaj?func=openurl&genre=article&issn=10255834&date=2010&volume=2010&issue=&spage=
Source: DOAJ

ABSTRACT It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a K-functional is needed. In the present paper, the upper bounds for the K-functional on the unit sphere are estimated with spherical harmonics approximation. The results show that convergence rate of the K-functional depends upon the smoothness of both the approximated function and the reproducing kernels.

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Keywords

approximated function
 
K-functional
 
reproducing kernel Hilbert spaces
 
reproducing kernels
 
smoothness
 
unit sphere
 
upper bounds
 
upper bounds estimate