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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The existence of efficient lattice rules for multidimensional numerical integration


Author: Harald Niederreiter
Journal: Math. Comp. 58 (1992), 305-314, S7
MSC: Primary 65D30; Secondary 11K45
MathSciNet review: 1106976
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Abstract: In this contribution to the theory of lattice rules for multidimensional numerical integration, we first establish bounds for various efficiency measures which lead to the conclusion that in the search for efficient lattice rules one should concentrate on lattice rules with large first invariant. Then we prove an existence theorem for efficient lattice rules of rank 2 with prescribed invariants, which extends an earlier result of the author for lattice rules of rank 1.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1106976-5
PII: S 0025-5718(1992)1106976-5
Article copyright: © Copyright 1992 American Mathematical Society