On the mean square weighted \(\mathcal {L}_2\) discrepancy of randomized digital nets in prime base

DOI10.1016/j.jco.2006.03.005zbMath1142.11345OpenAlexW2139068855MaRDI QIDQ855890

N. E. Zubov

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.2006.03.005

zbMATH Keywords

QMC algorithmrandomized digital netweighted \(\mathcal {L}_2\) discrepancy

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Irregularities of distribution, discrepancy (11K38) General theory of distribution modulo (1) (11K06)

Related Items

Point sets with optimal order of extreme and periodic discrepancy ⋮ Tractability properties of the weighted star discrepancy ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Point sets and sequences with small discrepancy
• Bounds for the weighted \(L^p\) discrepancy and tractability of integration
• Sequences, discrepancies and applications
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• The discrepancy and gain coefficients of scrambled digital nets.
• Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
• Explicit evaluations and reciprocity theorems for finite trigonometric sums
• Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration
• Constructions of \((t,m,s)\)-nets and \((t,s)\)-sequences
• A class of generalized Walsh functions
• On the mean square weighted L₂discrepancy of randomized digital (t,m,s)-nets over Z₂
• On irregularities of distribution
• Geometric discrepancy. An illustrated guide