In this paper, we consider approximation to derivatives of a function by using radial basis function interpolation. Most of well-known theories for this problem provide error analysis in terms of the so-called native space, say Cφ. However, if a basis function φ is smooth, the space Cφ is extremely small. Thus, the purpose of this study is to extend this result to functions in the homogenous Sobolev space.
Bibliographical noteFunding Information:
This work was supported by Korea Research Foundation Grant (KRF-2003-C00014).
- 'Shifted' surface spline
- Approximation power
- Homogeneous Sobolev space
- Radial basis function