About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 206265, 5 pages
http://dx.doi.org/10.1155/2013/206265
Research Article

Interpolation and Best Approximation for Spherical Radial Basis Function Networks

Institute for Information and System Sciences, School of Mathematics and statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China

Received 1 May 2013; Revised 17 September 2013; Accepted 18 September 2013

Academic Editor: Mieczysław Mastyło

Copyright © 2013 Shaobo Lin et al. 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

Within the conventional framework of a native space structure, a smooth kernel generates a small native space, and radial basis functions stemming from the smooth kernel are intended to approximate only functions from this small native space. In this paper, we embed the smooth radial basis functions in a larger native space generated by a less smooth kernel and use them to interpolate the samples. Our result shows that there exists a linear combination of spherical radial basis functions that can both exactly interpolate samples generated by functions in the larger native space and near best approximate the target function.