On the construction of optimal cubature formulae which use integrals over hyperspheres

Abstract

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. © 2007 Elsevier Inc. All rights reserved. 
DOI: 10.1016/j.jco.2007.02.002

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