This article is cited in 7 papers

Computational mathematics

Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D_{4h}}$

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk

Abstract: An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the dihedral group of rotations with inversion $\mathrm{D_{4h}}$ is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry group up to the 29th order of accuracy.

Keywords: numerical integration, invariant cubature formulas, invariant polynomials, dihedral group of rotations.

UDC: 519.644

MSC: 65D32

Received May 13, 2015, published September 9, 2015

DOI: 10.17377/semi.2015.12.039