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

@article{Yarotsky2013UnivariateIB,
  title={Univariate interpolation by exponential functions and Gaussian RBFs for generic sets of nodes},
  author={D. Yarotsky},
  journal={J. Approx. Theory},
  year={2013},
  volume={166},
  pages={163-175}
}
  • D. Yarotsky
  • Published 2013
  • Mathematics, Computer Science
  • J. Approx. Theory
  • 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. 
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