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Triangular canonical forms for lattice rules of prime-power order
Author(s):
J.
N.
Lyness;
S.
Joe.
Journal:
Math. Comp.
65
(1996),
165-178.
MSC (1991):
Primary 65D30, 65D32
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Abstract:
In this paper we develop a theory of  -cycle  representations for  -dimensional lattice rules of prime-power order. Of particular interest are canonical forms which, by definition, have a  -matrix consisting of the nontrivial invariants. Among these is a family of triangular forms, which, besides being canonical, have the defining property that their  -matrix is a column permuted version of a unit upper triangular matrix. Triangular forms may be obtained constructively using sequences of elementary transformations based on elementary matrix algebra. Our main result is to define a unique canonical form for prime-power rules. This ultratriangular form is a triangular form, is easy to recognize, and may be derived in a straightforward manner.
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Additional Information:
J.
N.
Lyness
Affiliation:
Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439
Email:
lyness@mcs.anl.gov
S.
Joe
Affiliation:
Department of Mathematics and Statistics, The University of Waikato, Private Bag 3105, Hamilton, New Zealand
Email:
stephenj@hoiho.math.waikato.ac.nz
DOI:
10.1090/S0025-5718-96-00691-6
PII:
S 0025-5718(96)00691-6
Received by editor(s):
August 16, 1994
Received by editor(s) in revised form:
February 17, 1995
Additional Notes:
This work was supported in part by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Computational and Technology Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.
Copyright of article:
Copyright
1996,
American Mathematical Society
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