Why do so many cubature formulae have so many positive weights?
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We consider cubature formulae which are invariant with respect to a transformation group and prove sufficient conditions for such formulae to have positive weights. This is worked out for different symmetries: we consider central symmetric, symmetric and fully symmetric cubature formulae. The theoretical results are illustrated with examples.
Subject classificationAMS(MOS) 65D32 CR G.1.4
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