Randomly shifted lattice rules for unbounded integrands

DOI10.1016/j.jco.2006.04.006zbMath1112.65003OpenAlexW2030336883MaRDI QIDQ855892

Benjamin J. Waterhouse, Frances Y. Kuo, Grzegorz W. Wasilkowski

Publication date: 7 December 2006

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

Full work available at URL: https://doi.org/10.1016/j.jco.2006.04.006

zbMATH Keywords

reproducing kernel Hilbert spacesquasi-Monte Carlo methodsmultivariate integrationworst case errorrandomly shifted lattice rulesmean square worst case error for randomly shifted rank-1 lattice rulesunbounded integrals

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical integration (65D30)

Related Items (16)

Shifted lattice rules based on a general weighted discrepancy for integrals over Euclidean space ⋮ QMC Galerkin Discretization of Parametric Operator Equations ⋮ A Monte Carlo Method for Integration of Multivariate Smooth Functions ⋮ Optimal algorithms for doubly weighted approximation of univariate functions ⋮ On the quasi-Monte Carlo method with Halton points for elliptic PDEs with log-normal diffusion ⋮ Some Results on the Complexity of Numerical Integration ⋮ Quasi-Monte Carlo for highly structured generalised response models ⋮ Quasi-Monte Carlo finite element methods for elliptic PDEs with lognormal random coefficients ⋮ Efficient multivariate approximation on the cube ⋮ 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 ⋮ Liberating the dimension ⋮ Transformed rank-1 lattices for high-dimensional approximation ⋮ Integration in Hermite spaces of analytic functions ⋮ On embeddings of weighted tensor product Hilbert spaces ⋮ Multilevel Quasi-Monte Carlo methods for lognormal diffusion problems

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