Numerical Algorithms

, Volume 39, Issue 1–3, pp 307–315 | Cite as

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

  • Francis J. Narcowich


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).


interpolation scattered data radial basis functions band-limited functions error estimates 


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© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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