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TW 309

R. Cools and K.J. Kim
Rotation invariant cubature formulas over the n-dimensional unit cube

Abstract

We consider cubature formulas to approximate multivariate integrals that remain unchanged under the orientation preserving transformation of a cube. The use of invariant theory (Molien series, Reynold operator) for the construction of such cubature formula is investigated. Some new cubature formulas for the unit cube that are obtained using this approach, are presented.