Component-by-component construction of good lattice rules with a composite number of points

DOI10.1006/jcom.2002.0650zbMath1022.65006OpenAlexW1991368063MaRDI QIDQ1872638

Frances Y. Kuo, Stephen Joe

Publication date: 14 May 2003

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

Full work available at URL: https://doi.org/10.1006/jcom.2002.0650

zbMATH Keywords

numerical resultsMonte Carlo methodslarge deviationshitting probabilitieslattice rulesrare event simulation

Mathematics Subject Classification ID

Monte Carlo methods (65C05)

Related Items (23)

Liberating the weights ⋮ Construction algorithms for good extensible lattice rules ⋮ Reducing the construction cost of the component-by-component construction of good lattice rules ⋮ Randomly shifted lattice rules for unbounded integrands ⋮ The construction of good extensible Korobov rules ⋮ On the convergence rate of the component-by-component construction of good lattice rules ⋮ Quasi-Monte Carlo tractability of high dimensional integration over products of simplices ⋮ Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights ⋮ Tractability of Multivariate Integration in Hybrid Function Spaces ⋮ Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces ⋮ My dream quadrature rule ⋮ Open problems for tractability of multivariate integration. ⋮ Variance bounds and existence results for randomly shifted lattice rules ⋮ On the distribution of integration error by randomly-shifted lattice rules ⋮ Ian Sloan and Lattice Rules ⋮ Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm ⋮ Construction of quasi-Monte Carlo rules for multivariate integration in spaces of permutation-invariant functions ⋮ Intermediate rank lattice rules and applications to finance ⋮ Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands ⋮ Good lattice rules in weighted Korobov spaces with general weights ⋮ Existence and construction of shifted lattice rules with an arbitrary number of points and bounded weighted star discrepancy for general decreasing weights ⋮ Quasi-Monte Carlo methods can be efficient for integration over products of spheres ⋮ The construction of good extensible rank-1 lattices

Cites Work

• 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
• Integration and approximation in arbitrary dimensions
• Error bounds for rank 1 lattice quadrature rules modulo composites
• 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
• Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces
• Theory of Reproducing Kernels
• Unnamed Item

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