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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On Cartesian products of good lattices
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by S. K. Zaremba PDF
Math. Comp. 30 (1976), 546-552 Request permission

Abstract:

Good lattices yield a powerful method of computing multiple integrals. Asymptotically, a lattice generated by one good lattice point is much more efficient than a Cartesian product of such lattices. However, if the number of dimensions is large, this does not always apply to the case when the number of points remains within reasonable limits. Examples of such products of two or three lattices being more efficient than good lattices generated by single lattice points are systematically presented. Additional symmetries of Cartesian products of lattices offer a further advantage when the integrand has to be symmetrized beforehand.
References
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 546-552
  • MSC: Primary 65D30
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0423770-X
  • MathSciNet review: 0423770