On the stationary Lp -approximation power to derivatives by radial basis function interpolation

Abstract

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. © 2003 Elsevier Inc. All rights reserved.