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 Sib. Zh. Vychisl. Mat., 2002, Volume 5, Number 3, Pages 267–274 (Mi sjvm254)

Minimal cubature formulae of an even degree for the 2-torus

M. V. Noskova, H. J. Schmidb

a Dept. of Applied Math., Krasnoyarsk State Tech. University
b Math. Institut, Universitat Erlangen-Nurnberg, Germany

Abstract: In this paper, we derive the minimal even degree formulas for the 2-torus in the trigonometric case. All such formulas are obtained by solving several matrix equations. As far as we know, this is the first approach to determine all formulae of this type. Computational results by using a Computer Algebra System are presented. They verify that up to degree 30 there is only one minimal formula of even degree (and its dual) if one node is fixed. In all the cases computed, it turned out that the known lattice rules of rank 1 are the only minimal formulas.

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Citation: M. V. Noskov, H. J. Schmid, “Minimal cubature formulae of an even degree for the 2-torus”, Sib. Zh. Vychisl. Mat., 5:3 (2002), 267–274

Citation in format AMSBIB
\Bibitem{NosSch02} \by M.~V.~Noskov, H.~J.~Schmid \paper Minimal cubature formulae of an even degree for the 2-torus \jour Sib. Zh. Vychisl. Mat. \yr 2002 \vol 5 \issue 3 \pages 267--274 \mathnet{http://mi.mathnet.ru/sjvm254} 

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This publication is cited in the following articles:
1. M. V. Noskov, H. J. Schmid, “Cubature formulas of high trigonometric accuracy”, Comput. Math. Math. Phys., 44:5 (2004), 740–749
2. N. N. Osipov, “On minimal cubature formulas with the trigonometric $d$-property in the two-dimensional case”, Comput. Math. Math. Phys., 45:1 (2005), 5–12
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