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

摘要

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