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

DOI:
https://doi.org/10.1090/S0025-5718-96-00767-3

MathSciNet review:
1361806

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Abstract | References | Similar Articles | Additional Information

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

MR Author ID:
51325

ORCID:
0000-0002-5567-5836

Email:
Ronald.Cools@cs.kuleuven.ac.be

**Ian H. Sloan**

Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2033, Australia

MR Author ID:
163675

ORCID:
0000-0003-3769-0538

Email:
i.sloan@unsw.edu.au

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