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

 

Minimal cubature formulae of
trigonometric degree


Authors: Ronald Cools and Ian H. Sloan
Journal: Math. Comp. 65 (1996), 1583-1600
MSC (1991): Primary 41A55, 41A63; Secondary 65D32
MathSciNet review: 1361806
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Abstract: In this paper we construct minimal cubature formulae of trigonometric degree: we obtain explicit formulae for low dimensions of arbitrary degree and for low degrees in all dimensions. A useful tool is a closed form expression for the reproducing kernels in two dimensions.


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Additional Information

Ronald Cools
Affiliation: Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200 A, B-3001 Heverlee, Belgium
Email: Ronald.Cools@cs.kuleuven.ac.be

Ian H. Sloan
Affiliation: School of Mathematics, University of New South Wales, Sydney NSW 2033, Australia
Email: i.sloan@unsw.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00767-3
PII: S 0025-5718(96)00767-3
Keywords: Cubature, trigonometric degree, lattice rules
Received by editor(s): September 15, 1993
Received by editor(s) in revised form: September 22, 1994, and August 28, 1995
Article copyright: © Copyright 1996 American Mathematical Society