Univariate interpolation by exponential functions and gaussian RBFs for generic sets of nodes
Numerical Analysis
2012-12-18 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.1205.5961,
title = {Univariate interpolation by exponential functions and gaussian RBFs for generic sets of nodes},
author = {Dmitry Yarotsky},
journal= {arXiv preprint arXiv:1205.5961},
year = {2012}
}
Comments
Some stylistic improvements and added references following feedback from the reviewers