The convergence rates of Shannon sampling learning algorithms

In the present paper, we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space （RKHS） derived by a Mercer kernel and a determined net. We show that if the sample is taken according to the determined set, then, the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net. The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator. The paper is an investigation on a remark provided by Smale and Zhou.