Cubature formulas on the sphere that are invariant under the transformations of the dihedral group of rotations D 4

摘要

An algorithm for nding the best cubature formulas (in a sense) on the sphere that are invariant under the transformations of the dihedral group of rotations D4 is described. This algorithm is applied for nding parameters of all the best cubature formulas of this symmetry type up to the 35th order of accuracy.