Duality theory and propagation rules for generalized digital nets

DOI10.1090/S0025-5718-09-02315-1zbMath1219.11115MaRDI QIDQ3584815

Peter Kritzer, Josef Dick

Publication date: 30 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

duality theorydigital netspropagation rules

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Linear codes (general theory) (94B05) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (11)

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions ⋮ QMC rules of arbitrary high order: Reproducing kernel Hilbert space approach ⋮ Existence of Higher Order Convergent Quasi-Monte Carlo Rules via Walsh Figure of Merit ⋮ Duality theory and propagation rules for higher order nets ⋮ An explicit construction of point sets with large minimum Dick weight ⋮ A computable figure of merit for quasi-Monte Carlo point sets ⋮ A higher order Blokh-Zyablov propagation rule for higher order nets ⋮ On the approximation of smooth functions using generalized digital nets ⋮ Discrepancy Theory and Quasi-Monte Carlo Integration ⋮ Propagation rules for \((u, m, \mathbf{e}, s)\)-nets and \((u, \mathbf{e}, s)\)-sequences ⋮ Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Uses Software

• MinT

Cites Work

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• Point sets and sequences with small discrepancy
• Matrix-product constructions of digital nets
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• Duality for digital nets and its applications
• Constructions of digital nets
• Equidistribution Properties of Generalized Nets and Sequences
• Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
• Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
• Coding‐theoretic constructions for (t,m,s)‐nets and ordered orthogonal arrays
• Matrix-product codes over \(\mathbb{F}_q\)

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