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

 

Notes on integration and integer sublattices


Authors: J. N. Lyness, T. Sørevik and P. Keast
Journal: Math. Comp. 56 (1991), 243-255
MSC: Primary 65D32
MathSciNet review: 1052101
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Abstract: A lattice rule is a quadrature rule over an s-dimensional hypercube, using N abscissas located on an integration lattice. In this paper we study sublattices and superlattices of integration lattices and of integer lattices. We exploit the properties of generator matrices of a lattice to provide an easy and elegant description of the relation between a lattice and a sublattice of given order. We also obtain necessary and sufficient criteria for existence of sublattices and information about the number of these.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1052101-8
PII: S 0025-5718(1991)1052101-8
Article copyright: © Copyright 1991 American Mathematical Society