A note on the CBC-DBD construction of lattice rules with general positive weights

DOI10.1016/J.JCO.2022.101721OpenAlexW4310817285MaRDI QIDQ2693683

Peter Kritzer

Publication date: 24 March 2023

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

Full work available at URL: https://arxiv.org/abs/2208.13610

zbMATH Keywords

numerical integrationlattice pointsweighted function spacescomponent-by-component constructionfast constructiondigit-by-digit construction

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items (1)

On a reduced component-by-component digit-by-digit construction of lattice point sets

Uses Software

• QMC4PDE

Cites Work

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• Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation
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• Tractability of multivariate problems. Volume I: Linear information
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces
• Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness
• Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
• Component-by-component construction of good lattice rules
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Lattice Rules
• High-dimensional integration: The quasi-Monte Carlo way

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