The Convergence Rate for a <inline-formula> <graphic file="1029-242X-2010-249507-i1.gif"/></inline-formula>-Functional in Learning Theory
<p/> <p>It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a <inline-formula> <graphic file="1029-242X-2010-249507-i2.gif"/></inline-formula>-functional is needed. In the present paper, the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/249507 |
| Summary: | <p/> <p>It is known that in the field of learning theory based on reproducing kernel Hilbert spaces the upper bounds estimate for a <inline-formula> <graphic file="1029-242X-2010-249507-i2.gif"/></inline-formula>-functional is needed. In the present paper, the upper bounds for the <inline-formula> <graphic file="1029-242X-2010-249507-i3.gif"/></inline-formula>-functional on the unit sphere are estimated with spherical harmonics approximation. The results show that convergence rate of the <inline-formula> <graphic file="1029-242X-2010-249507-i4.gif"/></inline-formula>-functional depends upon the smoothness of both the approximated function and the reproducing kernels.</p> |
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| ISSN: | 1025-5834 1029-242X |