In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then c...In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.展开更多
基金The research is supported by the National Natural Science Foundation under Grant No. 10471130 and the Zhejiang Province Science Foundation under Grant No. Y604003. Acknowledgements The author thanks the referees for giving valuable comments on this paper which make him rewrite this paper in a better form.
文摘In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.
