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An efficient composite formula for multidimensional quadrature

By Henry C. Thacher

Communications of the ACM, Vol. 7 No. 1, Pages 23-25

A (2s+1)-point, second-degree quadrature formula for integration over an s-dimensional hyper-rectangle is presented. All but one of the points lie on the surface with weights of opposite sign attached to points on opposite faces. When a large volume is subdivided into congruent rectangular subdivisions, only one point is required in each interior subdivision to achieve second-degree accuracy.

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