The construction of good extensible rank-1 lattices

DOI10.1090/S0025-5718-08-02009-7zbMath1211.11092MaRDI QIDQ3055074

Josef Dick, Benjamin J. Waterhouse, Friedrich Pillichshammer

Publication date: 7 November 2010

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

zbMATH Keywords

numerical integrationquasi-Monte Carlocomponent-by-component constructionextensible lattice rule

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Random number generation in numerical analysis (65C10) Numerical integration (65D30) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (22)

QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND ⋮ Exponential convergence and tractability of multivariate integration for Korobov spaces ⋮ Construction algorithms for good extensible lattice rules ⋮ Constructing lattice rules based on weighted degree of exactness and worst case error ⋮ On combined component-by-component constructions of lattice point sets ⋮ The construction of good extensible Korobov rules ⋮ On a projection-corrected component-by-component construction ⋮ Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm ⋮ Numerical integration in log-Korobov and log-cosine spaces ⋮ Lattice rules for nonperiodic smooth integrands ⋮ Extensible hyperplane nets ⋮ Ian Sloan and Lattice Rules ⋮ Weighted compound integration rules with higher order convergence for all \(N\) ⋮ Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients ⋮ Searching for extensible Korobov rules ⋮ Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation ⋮ Fast CBC construction of randomly shifted lattice rules achieving \(\mathcal{O}(n^{- 1 + \delta})\) convergence for unbounded integrands over \(\mathbb{R}^s\) in weighted spaces with POD weights ⋮ Randomly shifted lattice rules with the optimal rate of convergence for unbounded integrands ⋮ Construction algorithms for higher order polynomial lattice rules ⋮ Proof techniques in quasi-Monte Carlo theory ⋮ Multi-level quasi-Monte Carlo finite element methods for a class of elliptic PDEs with random coefficients ⋮ Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems

Cites Work

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