Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration

DOI10.1007/BF01298952zbMath0876.11042OpenAlexW2086236484MaRDI QIDQ1912217

Gerhard Larcher, Wolfgang Ch. Schmid, Harald Niederreiter

Publication date: 4 June 1996

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178723

zbMATH Keywords

error bounddigital netsdigital sequences\((t,m,s)\) nethigh-dimensional quasi-Monte Carlo integrationlow discrepancy point setsrapidly converging Walsh series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Numerical integration (65D30) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

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Cites Work

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• Point sets and sequences with small discrepancy
• Low-discrepancy and low-dispersion sequences
• Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes
• Point sets with uniformity properties and orthogonal hypercubes
• On the distribution of an analog to classical Kronecker-sequences
• Uniform convergence of Fourier series on groups. I
• A class of generalized Walsh functions
• Good Parameters for a Class of Node Sets in Quasi-Monte Carlo Integration
• 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 Numerical Integration of Walsh Series by Number-Theoretic Methods
• Representation of Functions as Walsh Series to Different Bases and an Application to the Numerical Integration of High-Dimensional Walsh Series
• Nets obtained from rational functions over finite fields
• Generalized (t, s)-Sequences, Kronecker-Type Sequences, and Diophantine Approximations of Formal Laurent Series
• Optimal Polynomials for (T,M,S)-Nets and Numerical Integration of Multivariate Walsh Series