Error estimates for interpolation of rough data using the scattered shifts of a radial basis function
Provides theoretical error bounds for rough data interpolation, addressing a gap in RBF theory for practitioners dealing with non-smooth functions.
This paper establishes error estimates for radial basis function interpolation when the function being interpolated is rough, extending previous results that assumed smooth functions in the native space.
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.