Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633056 | Applied Mathematics and Computation | 2009 | 9 Pages |
Abstract
In this paper, we study several radial basis function approximation schemes in Sobolev spaces. We obtain an optional error estimate by using a class of smoothing operators. We also discussed sufficient conditions for the smoothing operators to attain the desired approximation order. We then construct the smoothing operators by some compactly supported radial kernels, and use them to approximate Sobolev space functions with optimal convergence order. These kernels can be simply constructed and readily applied to practical problems. The results show that the approximation power depends on the precision of the sampling instrument and the density of the available data.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Limin Ma, Zongmin Wu,