An Efficient Composite Formula for Multidimensional Quadrature 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. CACM January, 1964 Thacher Jr., H. C. CA640109 JB March 10, 1978 5:28 AM 1146 4 1146 1146 5 1146 1146 5 1146 1146 5 1146 386 5 1146