Notes on integration and integer sublattices

Lyness, J. N.; Sørevik, T.; Keast, P.

doi:10.1090/S0025-5718-1991-1052101-8

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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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