Weighted geometric discrepancies and numerical integration on reproducing kernel Hilbert spaces

DOI10.1016/j.jco.2011.02.003zbMath1333.11073OpenAlexW2139493792MaRDI QIDQ657645

Michael Gnewuch

Publication date: 10 January 2012

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

Full work available at URL: https://doi.org/10.1016/j.jco.2011.02.003

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical integration (65D30) Irregularities of distribution, discrepancy (11K38)

Related Items (11)

Entropy, Randomization, Derandomization, and Discrepancy ⋮ Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold ⋮ Asymptotic behavior of average \(L_p\)-discrepancies ⋮ On weighted Hilbert spaces and integration of functions of infinitely many variables ⋮ Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence ⋮ Weighted discrepancy and numerical integration in function spaces ⋮ Infinite-dimensional integration and the multivariate decomposition method ⋮ Curve based approximation of measures on manifolds by discrepancy minimization ⋮ Infinite-dimensional integration on weighted Hilbert spaces ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration ⋮ Calculation of Discrepancy Measures and Applications

Cites Work

• Tractability of infinite-dimensional integration in the worst case and randomized settings
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• Relaxed verification for continuous problems
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Error reduction techniques in quasi-Monte Carlo integration.
• The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
• Average case complexity of multivariate integration
• Quasi-Random Sequences and Their Discrepancies
• A generalized discrepancy and quadrature error bound
• On tractability of weighted integration over bounded and unbounded regions in ℝ^{𝕤}
• Some applications of multidimensional integration by parts
• Theory of Reproducing Kernels
• Geometric discrepancy. An illustrated guide
• Intractability results for integration and discrepancy
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