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A Discrepancy-Based Analysis of Figures of Merit for Lattice Rules

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Monte-Carlo and Quasi-Monte Carlo Methods 1998

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Abstract

Classical figures of merit for choosing quasi-Monte Carlo methods for integration over thes-dimensional unit cube are the L p star discrepancy of the corresponding set of quadrature points and, when considering periodic integrands, Pα— usually withα an even positive integer. Hickernell (1998) introduced a generalised notion of discrepancy of which both these figures of merit are special cases. In this paper Hickernell’s decomposition of generalised discrepancy into lower-dimensional components is used to characterise differences between reported results achieved by rules selected according to these figures of merit. A further extension with application to rank-1 lattice rules and their k s copies is also described.

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Author information

Authors and Affiliations

  1. University of Technology, Sydney, PO Box 123, Broadway NSW 2007, Australia

    T. N. Langtry

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  1. T. N. Langtry
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Editors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010, Vienna, Austria

    Harald Niederreiter

  2. Claremont Graduate University, 925 N. Dartmouth Avenue, 91711, Claremont, CA, USA

    Jerome Spanier

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© 2000 Springer-Verlag Berlin Heidelberg

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Langtry, T.N. (2000). A Discrepancy-Based Analysis of Figures of Merit for Lattice Rules. In: Niederreiter, H., Spanier, J. (eds) Monte-Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59657-5_20

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  • DOI: https://doi.org/10.1007/978-3-642-59657-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66176-4

  • Online ISBN: 978-3-642-59657-5

  • eBook Packages: Springer Book Archive

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