A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights

DOI10.1016/j.cam.2014.08.017zbMath1300.65004arXiv1404.5497OpenAlexW2057875268MaRDI QIDQ458162

Gunther Leobacher, Josef Dick, Peter Kritzer, Friedrich Pillichshammer

Publication date: 7 October 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.5497

zbMATH Keywords

numerical integrationquasi-Monte Carlo methodsquadrature rulesnumerical resultcomponent-by-component algorithmpolynomial lattice rulesweighted reproducing kernel Hilbert spaces

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items

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Cites Work

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• On the convergence rate of the component-by-component construction of good lattice rules
• Tractability of multivariate problems. Volume II: Standard information for functionals.
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability of multivariate integration for weighted Korobov classes
• Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
• Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
• Integration and approximation in arbitrary dimensions
• Lattice rules for nonperiodic smooth integrands
• Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
• Good lattice rules in weighted Korobov spaces with general weights
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Factoring Finite Factor Rings
• A generalized discrepancy and quadrature error bound
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Construction algorithms for polynomial lattice rules for multivariate integration
• Polynomial Lattice Point Sets
• High-dimensional integration: The quasi-Monte Carlo way
• Theory of Reproducing Kernels