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Abstract and Applied Analysis
Volume 2014, Article ID 781068, 10 pages
http://dx.doi.org/10.1155/2014/781068
Research Article

Strong Inequalities for Hermite-Fejér Interpolations and Characterization of -Functionals

Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China

Received 10 October 2013; Accepted 6 December 2013; Published 16 January 2014

Academic Editor: Ding-Xuan Zhou

Copyright © 2014 Gongqiang You. 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

The works of Smale and Zhou (2003, 2007), Cucker and Smale (2002), and Cucker and Zhou (2007) indicate that approximation operators serve as cores of many machine learning algorithms. In this paper we study the Hermite-Fejér interpolation operator which has this potential of applications. The interpolation is defined by zeros of the Jacobi polynomials with parameters , . Approximation rate is obtained for continuous functions. Asymptotic expression of the -functional associated with the interpolation operators is given.