Abstract
Error estimates for scattered-data interpolation via radial basis functions (RBFs) for target functions in the associated reproducing kernel Hilbert space (RKHS) have been known for a long time. Recently, these estimates have been extended to apply to certain classes of target functions generating the data which are outside the associated RKHS. However, these classes of functions still were not "large" enough to be applicable to a number of practical situations. In this paper we obtain Sobolev-type error estimates on compact regions of Rn when the RBFs have Fourier transforms that decay algebraically. In addition, we derive a Bernstein inequality for spaces of finite shifts of an RBF in terms of the minimal separation parameter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Narcowich, F., Ward, J. & Wendland, H. Sobolev Error Estimates and a Bernstein Inequality for Scattered Data Interpolation via Radial Basis Functions. Constr Approx 24, 175–186 (2006). https://doi.org/10.1007/s00365-005-0624-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00365-005-0624-7