Onp-generator fully symmetric quadrature rules

Summary We consider fully symmetric quadrature rules for fully symmetricn-dimensional integration regions. When the region is a product region it is well known that product Gaussian rules exist. These obtain an approximation of polynomial degree 4p+1 based on (2p+1)ⁿ function values arranged on a rectangular grid. We term rules using such a grid,p-generator rules. In this paper we determine the necessary conditions on the region of integration forp-generator rules of degree 4p+1 to exist. Regions with this property are termed PropertyQ regions and besides product spaces, this class includes the hypersphere and other related regions.Work performed under the auspices of the U.S. Energy Research and Development Administration