  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.
