Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 249507, 18 pages
doi:10.1155/2010/249507
Research Article

The Convergence Rate for a K-Functional in Learning Theory

Bao-Huai Sheng1 and Dao-Hong Xiang2

1Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, China
2Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China

Received 11 November 2009; Accepted 21 February 2010

Academic Editor: Yuming Xing

Copyright © 2010 Bao-Huai Sheng and Dao-Hong Xiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.