Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 964528, 10 pages
doi:10.1155/2010/964528
Research Article

Positive Approximation and Interpolation Using Compactly Supported Radial Basis Functions

Jinming Wu, Xiaolei Zhang, and Lihui Peng

College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

Received 17 July 2009; Revised 27 December 2009; Accepted 21 February 2010

Academic Editor: Victoria Vampa

Copyright © 2010 Jinming Wu 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

We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the proposed method is flexible.