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Mathematics of Computation

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On Cartesian products of good lattices


Author: S. K. Zaremba
Journal: Math. Comp. 30 (1976), 546-552
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1976-0423770-X
MathSciNet review: 0423770
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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.


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DOI: https://doi.org/10.1090/S0025-5718-1976-0423770-X
Article copyright: © Copyright 1976 American Mathematical Society