Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions Academic Article

abstract

• The purpose of this paper is to get error estimates for spherical basis function (SBF) interpolation and approximation for target functions in Sobolev spaces less smooth than the SBFs, and to show that the rates achieved are, in a sense, best possible. In addition, we establish a Bernstein-type theorem, where the smallest separation between data sites plays the role of a Nyquist frequency. We then use these Berstein-type estimates to derive inverse estimates for interpolation via SBFs. 2006 Springer.

authors

• Narcowich, Francis
• Ward, Joseph

published proceedings

• FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

author list (cited authors)

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

citation count

• 51

complete list of authors

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

publication date

• July 2007

publisher

• Springer Nature  Publisher

published in

• Foundations of Computational Mathematics  Journal

keywords

• Bernstein Theorem
• Error Estimates
• Inverse Theorem
• Radial Basis Functions
• Scattered Data
• Spherical Basis Functions

Digital Object Identifier (DOI)

• 10.1007/s10208-005-0197-7

start page

• 369

end page

• 390

volume

• 7

issue

• 3

URL

• http://dx.doi.org/10.1007/s10208-005-0197-7