Radial Basis Function Approximation on R^d
John Paul Ward, Houston Univ., Texas, USA

Seminar • 21 February 2011

Abstract
In approximation theory, two important types of estimates are direct theorems and inverse theorems. The former bound the error of an approximation method, while the latter are used to classify functions based on approximation rates. Both results are equally important, and when combined, they can be used to characterize smoothness spaces in terms of an approximation procedure. This talk will cover both types of theorems applied to radial basis function (RBF) approximation on $\mathbb{R}^d$. Specifically, we will examine a general method for finding $L^p$ error estimates for approximation by RBFs that are ``close'' to Green's functions, and we will apply this method to find rates for some popular RBFs. This will be followed by a derivation of inverse estimates for RBFs with finite smoothness.