Abstract
A lattice rule is a particular kind of multidimensional quadrature rule for numerical integration over the unit s-dimensional cube. Recently Sloan and Lyness have classified all lattice rules according to their “rank”. For example, the number-theoretic rules of Korobov and Conroy have rank 1, and the product-trapezoidal rule has rank s. In this paper we first give a brief review of lattice rules and the concept of rank, and then give preliminary results of a computer search for “good” lattice rules of rank 2.
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References
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Sloan, I.H. and Walsh, L. (1988) A computer search of rank-2 lattice rules for multidimensional quadrature, in preparation.
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© 1988 Springer Basel AG
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Sloan, I.H., Walsh, L. (1988). Lattice Rules — Classification and Searches. In: Braß, H., Hämmerlin, G. (eds) Numerical Integration III. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 85. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6398-8_23
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DOI: https://doi.org/10.1007/978-3-0348-6398-8_23
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2205-2
Online ISBN: 978-3-0348-6398-8
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