Univariate interpolation by exponential functions and gaussian RBFs for generic sets of nodes

Abstract

We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the Harish-Chandra-Itzykson-Zuber formula. We then prove the exponential convergence of interpolation for functions analytic in a sufficiently large domain. As an application, we prove the global exponential convergence of optimization by expected improvement for such functions.