Reducing the construction cost of the component-by-component construction of good lattice rules

DOI10.1090/S0025-5718-03-01610-7zbMath1051.65003OpenAlexW2086574596MaRDI QIDQ4813619

Frances Y. Kuo, Josef Dick

Publication date: 13 August 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01610-7

zbMATH Keywords

algorithmconvergencenumerical exampleserror boundshiftsrank-1 lattice rulesquasi-Monte-Carlo methodcomponent-by-component\(d\)-dimensional rules

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

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Cites Work

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• On the convergence rate of the component-by-component construction of good lattice rules
• 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
• Component-by-component construction of good lattice rules with a composite number of points
• Component-by-component construction of good lattice rules
• On the step-by-step construction of quasi--Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
• Applications of Number Theory to Numerical Analysis
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Theory of Reproducing Kernels

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