Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions Academic Article

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. 2006 Springer Science+Business Media, Inc.

authors

• Narcowich, Francis
• Ward, Joseph

published proceedings

• CONSTRUCTIVE APPROXIMATION

altmetric score

• 3

author list (cited authors)

• Narcowich, F. J., Ward, J. D., & Wendland, H.

citation count

• 87

complete list of authors

• Narcowich, Francis J||Ward, Joseph D||Wendland, Holger

publication date

• September 2006

publisher

• Springer Nature  Publisher

published in

• Constructive Approximation  Journal

keywords

• Band-limited Functions
• Bernstein Inequality
• Error Estimates
• Radial Basis Functions
• Scattered Data

Digital Object Identifier (DOI)

• 10.1007/s00365-005-0624-7

start page

• 175

end page

• 186

volume

• 24

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs00365-005-0624-7