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

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.Comment: Some stylistic improvements and added references following feedback from the reviewer

Sequential search strategies based on kriging

This manuscript has been written to obtain the French Habilitation à Diriger des Recherches. It is not intended to provide new academic results nor should it be considered as a reference textbook. Instead, this manuscript is a brief (and incomplete) summary of my teaching and research activities. You will find in this manuscript a compilation of some articles in which I had a significant contribution, together with some introductory paragraphs about sequential search strategies based on kriging