Cubature formulas for the surface of the sphere

摘要

Null space arguments are used to derive feasible structures for integration formulas on the surface of the s-dimensional sphere. Structures are obtained, for s = 3 and s = 4 for formulas of degrees 3 to 17, and for general s of degrees 3 to 9. Several new formulas in dimension 4 and for arbitrary dimension are constructed.