Uniform distribution, discrepancy, and reproducing kernel Hilbert spaces

DOI10.1006/jcom.2001.0580zbMath1001.46015OpenAlexW2014177530MaRDI QIDQ5949381

Peter Zinterhof, Clemens Amstler

Publication date: 11 December 2002

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcom.2001.0580

zbMATH Keywords

numerical integrationdiscrepancyuniform distributionreproducing kernel Hilbert space

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical integration (65D30)

Related Items (5)

QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere ⋮ Statistical properties of $b$-adic diaphonies ⋮ Some current issues in quasi-Monte Carlo methods ⋮ Quasi-Monte Carlo integration on manifolds with mapped low-discrepancy points and greedy minimal Riesz \(s\)-energy points ⋮ Theory of generalized discrepancies on a ball of arbitrary finite dimensions and algorithms for finding low-discrepancy point sets

Cites Work

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• Sequences, discrepancies and applications
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Discrepancy operators and numerical integration on compact groups
• Some remarks on a discrepancy in compact groups
• Integration and approximation in arbitrary dimensions
• Computing discrepancies of Smolyak quadrature rules
• Theory of Reproducing Kernels

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