Recent developments in error estimates for scattered-data interpolation via radial basis functions Academic Article

abstract

• Error estimates for scattered data interpolation by "shifts" of a positive definite function for target functions in the associated reproducing kernel Hilbert space (RKHS) have been known for a long time. However, apart from special cases where data is gridded, these interpolation estimates do not apply when the target functions generating the data are outside of the associated RKHS, and in fact until very recently no estimates were known in such situations. In this paper, we review these estimates in cases where the underlying space is Rn and the positive definite functions are radial basis functions (RBFs). Springer 2005.

authors

• Narcowich, Francis

published proceedings

• NUMERICAL ALGORITHMS

author list (cited authors)

• Narcowich, F. J.

citation count

• 9

complete list of authors

• Narcowich, FJ

publication date

• July 2005

publisher

• Springer Nature  Publisher

published in

• Numerical Algorithms  Journal

keywords

• Band-limited Functions
• Error Estimates
• Interpolation
• Radial Basis Functions
• Scattered Data

Digital Object Identifier (DOI)

• 10.1007/s11075-004-3644-7

start page

• 307

end page

• 315

volume

• 39

issue

• 1-3