The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets

DOI10.1007/s00211-006-0046-xzbMath1111.65002OpenAlexW1976420124MaRDI QIDQ861659

N. E. Zubov

Publication date: 30 January 2007

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-006-0046-x

zbMATH Keywords

Walsh functionsworst-case errorKorobov polynomial lattice rules(t,m,s)-nets, polynomial lattice rulesdigital shiftfolded point setmean square worst-case errorreproducing kernel Sobolev space

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Irregularities of distribution, discrepancy (11K38) Well-distributed sequences and other variations (11K36) General theory of distribution modulo (1) (11K06) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (6)

Lattice rules for nonperiodic smooth integrands ⋮ Hilbert space with reproducing kernel and uniform distribution preserving maps. I ⋮ Constructing good higher order polynomial lattice rules with modulus of reduced degree ⋮ Quasi-Monte Carlo methods with applications in finance ⋮ Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration ⋮ The \(b\)-adic tent transformation for quasi-Monte Carlo integration using digital nets

Cites Work

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• Point sets and sequences with small discrepancy
• When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
• Tractability of multivariate integration for weighted Korobov classes
• The discrepancy and gain coefficients of scrambled digital nets.
• Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces
• Constructions of \((t,m,s)\)-nets and \((t,s)\)-sequences
• A class of generalized Walsh functions
• Discrépance de suites associées à un système de numération (en dimension s)
• Low-discrepancy point sets obtained by digital constructions over finite fields
• On the mean square weighted L₂discrepancy of randomized digital (t,m,s)-nets over Z₂
• Construction algorithms for polynomial lattice rules for multivariate integration
• Cyclic Digital Nets, Hyperplane Nets, and Multivariate Integration in Sobolev Spaces

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