Error estimates of quasi-interpolation and its derivatives

Authors:
Zhixiang Chen;Feilong Cao;Jinjie Hu
Affiliations:
Department of Mathematics, Shaoxing University, Shaoxing 312000, Zhejiang Province, PR China;Department of Mathematics, China Jiliang University, Hangzhou 310018, Zhejiang Province, PR China;Department of Mathematics, Shaoxing University, Shaoxing 312000, Zhejiang Province, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 5
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Abstract

Quasi-interpolation of radial basis functions on finite grids is a very useful strategy in approximation theory and its applications. A notable strongpoint of the strategy is to obtain directly the approximants without the need to solve any linear system of equations. For radial basis functions with Gaussian kernel, there have been more studies on the interpolation and quasi-interpolation on infinite grids. This paper investigates the approximation by quasi-interpolation operators with Gaussian kernel on the compact interval. The approximation errors for two classes of function with compact support sets are estimated. Furthermore, the approximation errors of derivatives of the approximants to the corresponding derivatives of the approximated functions are estimated. Finally, the numerical experiments are presented to confirm the accuracy of the approximations.