The discrepancy and gain coefficients of scrambled digital nets.

DOI10.1006/jcom.2001.0630zbMath1114.11306OpenAlexW2090893802MaRDI QIDQ1599197

Rong-Xian Yue, Fred J. Hickernell

Publication date: 5 June 2002

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

Full work available at URL: https://doi.org/10.1006/jcom.2001.0630

zbMATH Keywords

Monte Carlo methodslow discrepancy sequencesquadrature rulesdigital sequencesquasi Monte Carlo methodsscrambled digital nets

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (14)

The distribution of the discrepancy of scrambled digital (\(t\),\(m\),\(s\))-nets ⋮ \(I\)-binomial scrambling of digital nets and sequences ⋮ On the mean square weighted \(\mathcal {L}_2\) discrepancy of randomized digital nets in prime base ⋮ The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets ⋮ My dream quadrature rule ⋮ A Tool for Custom Construction of QMC and RQMC Point Sets ⋮ Improved bounds on the gain coefficients for digital nets in prime power base ⋮ Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands ⋮ A construction of polynomial lattice rules with small gain coefficients ⋮ Local antithetic sampling with scrambled nets ⋮ Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces ⋮ Control variates for quasi-Monte Carlo (with comments and rejoinder) ⋮ Optimal quadrature for Haar wavelet spaces ⋮ Constructions of \((t,m,s)\)-nets and \((t,s)\)-sequences

Uses Software

• Algorithm 823

Cites Work

• Low-discrepancy and low-dispersion sequences
• Random and quasi-random point sets
• Scrambling Sobol' and Niederreiter-Xing points
• On the \(L_2\)-discrepancy for anchored boxes
• The price of pessimism for multidimensional quadrature
• The microstructure of \((t,m,s)\)-nets
• Scrambled net variance for integrals of smooth functions
• On the variance of quadrature over scrambled nets and sequences
• Discrépance de suites associées à un système de numération (en dimension s)
• A generalized discrepancy and quadrature error bound
• Monte Carlo Variance of Scrambled Net Quadrature
• The Mean Square Discrepancy of Scrambled (t,s)-Sequences
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The discrepancy and gain coefficients of scrambled digital nets.