Existence and construction of shifted lattice rules with an arbitrary number of points and bounded weighted star discrepancy for general decreasing weights

DOI10.1016/j.jco.2011.02.001zbMath1235.65007OpenAlexW2047549016MaRDI QIDQ555032

Vasile Sinescu, Pierre L'Ecuyer

Publication date: 22 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.jco.2011.02.001

zbMATH Keywords

numerical integrationquasi-Monte Carlo methodtractabilitystar discrepancycomponent-by-component constructionrank-1 lattice ruleshigh-dimensional integrals

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items

QUASI-MONTE CARLO METHODS FOR HIGH-DIMENSIONAL INTEGRATION: THE STANDARD (WEIGHTED HILBERT SPACE) SETTING AND BEYOND, Construction Schemes for Weighted Lattice Rules, On the Choice of Weights in a Function Space for Quasi-Monte Carlo Methods for a Class of Generalised Response Models in Statistics, On equivalence of weighted anchored and ANOVA spaces of functions with mixed smoothness of order one in \(L_1\) or \(L_\infty\), Random weights, robust lattice rules and the geometry of the \(cbcrc\) algorithm, Variance bounds and existence results for randomly shifted lattice rules, On the distribution of integration error by randomly-shifted lattice rules, Optimal multilevel randomized quasi-Monte-Carlo method for the stochastic drift-diffusion-Poisson system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liberating the dimension
• Infinite-dimensional quadrature and approximation of distributions
• Shifted lattice rules based on a general weighted discrepancy for integrals over Euclidean space
• Construction algorithms for good extensible lattice rules
• Tractability of quasilinear problems. I: General results
• Quasi-Monte Carlo methods with applications in finance
• Multi-level Monte Carlo algorithms for infinite-dimensional integration on \(\mathbb R^{\mathbb N}\)
• Existence of good lattice points in the sense of Hlawka
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• The existence of good extensible rank-1 lattices
• Component-by-component construction of good lattice rules with a composite number of points
• Finite-order weights imply tractability of multivariate integration
• Fast component-by-component construction of rank-1 lattice rules with a non-prime number of points
• Good lattice rules in weighted Korobov spaces with general weights
• Component-by-component construction of good lattice rules
• Variance Reduction via Lattice Rules
• On the step-by-step construction of quasi--Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces
• The error bounds and tractability of quasi-Monte Carlo algorithms in infinite dimension
• Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces
• Good lattice rules based on the general weighted star discrepancy
• A generalized discrepancy and quadrature error bound
• Quadrature Error Bounds with Applications to Lattice Rules