Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

Details Error estimates for interpolation of rough data using the scattered shifts of a radial basis function Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

2007-05-30

arxiv.org/abs/0705.4300v1

Numer. Algorithms, 39(1-3):57-68, 2005

Mathematics

Numerical Analysis

12 pages

Scientific paper

10.1007/s11075-004-3620-2

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.

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