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Computational Investigations of Low-Discrepancy Point Sets II

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Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing

Part of the book series: Lecture Notes in Statistics ((LNS,volume 106))

Abstract

Point sets and sequences with small L2, discrepancy are useful in the evaluation of multiple integrals. For example, the average error in integration of all continuous functions over the unit cube (with respect to the Wiener measure) is given by the L2 discrepancy of the point set being used. [6] The Koksma-Hlawka inequality and Zaremba’s related inequality also imply the usefulness of low-discrepancy point sets. [4,7]

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References

  1. Faure, Henri: Good permutations for extreme discrepancy, J. Num. Theory, 42 (1992) 47 – 56.

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  5. Warnock, T. T.: Computational investigations of low-discrepancy point sets, in S. K. Zaremba (Ed.), Applications of Number Theory to Numerical Analysis, Academic Press, New York (1972) 319 – 343.

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  6. Woźniakowski, H.: Average case complexity of multivariate integration, Bull. Am. Math. Soc. 84 (1991) 185 – 194.

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Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, Los Alamos, NM, 87544, USA

    Tony T. Warnock

Authors
  1. Tony T. Warnock
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Editors and Affiliations

  1. Institüt für Informationsverabeitung, Osterreichische Akademie der Wissenschaften, Sonnenfelsgasse 19/2, A-1010, Wien, Austria

    Harald Niederreiter

  2. Department of Mathematical Sciences, University of Nevada, Las Vegas, 89154, Las Vegas, Nevada, USA

    Peter Jau-Shyong Shiue

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© 1995 Springer-Verlag New York, Inc.

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Warnock, T.T. (1995). Computational Investigations of Low-Discrepancy Point Sets II. In: Niederreiter, H., Shiue, P.JS. (eds) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Lecture Notes in Statistics, vol 106. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2552-2_23

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  • DOI: https://doi.org/10.1007/978-1-4612-2552-2_23

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94577-4

  • Online ISBN: 978-1-4612-2552-2

  • eBook Packages: Springer Book Archive

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