Gauss-Hermite quadratures for functions from Hilbert spaces with Gaussian reproducing kernels

DOI10.1007/s10543-011-0358-9zbMath1247.65034OpenAlexW1990166848MaRDI QIDQ438718

Henryk Woźniakowski, Frances Y. Kuo

Publication date: 31 July 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-011-0358-9

zbMATH Keywords

Hermite polynomialsGauss-Hermite quadraturereproducing kernel Hilbert spaceGaussian kernelexponential rate of convergenceexplicit error formulaintegration with Gaussian weight

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (5)

Multivariate integration for analytic functions with Gaussian kernels ⋮ Randomized approximation numbers on Besov classes with mixed smoothness ⋮ Gaussian kernel quadrature at scaled Gauss-Hermite nodes ⋮ A universal envelope for Gaussian processes and their kernels ⋮ Integration in reproducing kernel Hilbert spaces of Gaussian kernels

Uses Software

• Matlab
• ElemStatLearn

Cites Work

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• Is Gauss quadrature optimal for analytic functions?
• Interpolation of spatial data. Some theory for kriging
• On Dimension-independent Rates of Convergence for Function Approximation with Gaussian Kernels
• Learning Theory
• Kernel techniques: From machine learning to meshless methods
• An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels
• Radial Basis Functions
• Scattered Data Approximation

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