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Numerical Integration in High Dimensions — the Lattice Rule Approach

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Numerical Integration

Part of the book series: NATO ASI Series ((ASIC,volume 357))

Abstract

Of the few methods available for numerical integration in high dimensions, one of the most interesting is the number theoretic method of good lattice points originated by Korobov and Hlawka. This paper introduces the subject of lattice rules, which may be thought of as a generalisation of the method of good lattice points, and reviews recent developments. After introducing the concept of the rank of a lattice rule (the method of good lattice points has rank 1, the product-rectangle rule in s dimensions has rank s, and rules with every rank between 1 and s also exist) the paper will discuss some theoretical and practical grounds for believing that certain rules with rank greater than 1 might be of practical value.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of New South Wales, Kensington, NSW, 2033, Australia

    Ian H. Sloan

Authors
  1. Ian H. Sloan
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Terje O. Espelid

  2. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, USA

    Alan Genz

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© 1992 Springer Science+Business Media Dordrecht

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Sloan, I.H. (1992). Numerical Integration in High Dimensions — the Lattice Rule Approach. In: Espelid, T.O., Genz, A. (eds) Numerical Integration. NATO ASI Series, vol 357. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2646-5_5

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  • DOI: https://doi.org/10.1007/978-94-011-2646-5_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5169-9

  • Online ISBN: 978-94-011-2646-5

  • eBook Packages: Springer Book Archive

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