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

TL;DR

This paper develops error estimates for radial basis function interpolation when the target function is notably rough, extending existing analysis beyond smooth functions within the native space.

Contribution

It provides new error bounds for interpolating rough functions using scattered shifts of radial basis functions, broadening the applicability of RBF interpolation analysis.

Findings

Error estimates for rough data interpolation are established.

The analysis extends to functions outside the native space.

Results demonstrate the effectiveness of RBF interpolation for less smooth functions.

Abstract

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.