This article is cited in 4 papers

Computational mathematics

Cubature formulas on a sphere that are invariant under the transformations of the dihedral group of rotations with inversion $D_{3d}$

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6, Akad. Lavrent'eva ave., Novosibirsk, 630090, Russia

Abstract: An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the transformations of the dihedral group of rotations with inversion D3d is described. This algorithm is applied to find the parameters of all the best cubature formulas of this symmetry type up to the 35th order of accuracy.

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

UDC: 519.644

MSC: 65D32

Received February 21, 2019, published September 2, 2019

DOI: 10.33048/semi.2019.16.081

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