Scattered-Data Interpolation on $\bb R^protectn$: Error Estimates for Radial Basis and Band-Limited Functions Academic Article uri icon

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. However, apart from settings where data is gridded, these estimates do not apply when the target functions generating the data are outside of the associated RKHS, and, in fact, no estimates were known in such situations. In this paper, we deal with these cases, obtaining Sobolevtype error estimates on compact regions of ℝnwhen the RBFs have Fourier transforms that decay algebraically. In addition, we show that it is possible to construct band-limited interpolants that are also near-best approximants to such functions, with the band size being inversely proportional to the minimal separation of the data sites. © 2004 Society for Industrial and Applied Mathematics.

author list (cited authors)

  • Narcowich, F. J., & Ward, J. D.

citation count

  • 22

publication date

  • January 2004