Total positivity, spherical series, and hypergeometric functions of matrix argu ment
Journal of Approximation Theory - On Total Positivity and Applications, Part II
Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation
Journal of Approximation Theory
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation
SIAM Journal on Numerical Analysis
The Runge phenomenon and spatially variable shape parameters in RBF interpolation
Computers & Mathematics with Applications
Convergence Rates of Efficient Global Optimization Algorithms
The Journal of Machine Learning Research
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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.