Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4609075 | Journal of Complexity | 2008 | 18 Pages |
Abstract
In the present paper, we investigate the estimates for the covering number of a ball in a Mercer kernel Hilbert space on [0,1][0,1]. Let Pl(x)Pl(x) be the Legendre orthogonal polynomial of order l , al>0al>0 be real numbers satisfying ∑l=0+∞lal<+∞. Then, for the Mercer kernel functionK(x,t)=∑l=0+∞alPl(x)Pl(t),x,t∈[0,1],we provide the upper estimates of the covering number for the Mercer kernel Hilbert space reproducing from K(x,t)K(x,t). For some particular alal we give the lower estimates. Meanwhile, a kind of l2l2-norm estimate for the inverse Mercer matrix associated with the Mercer kernel K(x,t)K(x,t) is given.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Sheng Baohuai, Wang Jianli, Li Ping,