This article is cited in 2 papers

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

M. V. Noskov^a, H. J. Schmid<sup>b

a</sup> 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.

UDC: 519.644.7

Received: 22.10.2001
Revised: 26.11.2001

Language: English