Error estimates of quasi-interpolation and its derivatives

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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.

MSC

41A25
41A46
41A65
D05

Keywords

Error estimate
Quasi-interpolation
Approximation
Fourier transform
Modulus of continuity

Cited by (0)

This research was supported by the National Natural Science Foundation of China(Nos. 90818020, 61179041) and the Foundation of Innovation Team of Science and Technology of Zhejiang Province of China (No. 2009R50024).