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.

Some stylistic improvements and added references following feedback from the reviewers

References in corpus (2)

• Convergence rates of efficient global optimization algorithms
• Examples of inconsistency in optimization by expected improvement

Cited by in corpus (2)

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