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On the construction of optimal cubature formulae which use integrals over hyperspheres. (English) Zbl 1114.41019
Summary: We consider formulae of approximate integration over a \(d\)-dimensional ball which use \(n\) surface integrals along \((d-1)\)-dimensional spheres centered at the origin. For a class of functions defined on the ball with gradients satisfying an integral restriction, optimal formulae of this type are obtained.

MSC:
41A55 Approximate quadratures
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