Cubature formulas on the sphere that are invariant under the cyclic rotation groups C_kh

Cubature formulas on the sphere that are invariant under the cyclic rotation groups $C_{kh}$

Popov A. S.
Siberian Electronic Mathematical Reports, 22, 1, pp. 395-403 (2025)

УДК 519.644 
DOI: 10.33048/semi.2025.22.026  
MSC 65D32


Abstract:

An algorithm for finding the best cubature formulas (in a sense) on the sphere that are invariant under the transformations of the cyclic rotation groups $C_{kh}$ is described. This algorithm is applied for finding the parameters of the best cubature formulas of 19th and 31st orders of accuracy.

 

Keywords: numerical integration, invariant cubature formulas, invariant polynomials, cyclic rotation group.