This article is cited in 2 papers

Computational mathematics

Cubature formulas on the sphere that are invariant under the transformations of the dihedral groups of rotations with inversion

A. S. Popov

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

Abstract: An algorithm for finding the best cubature formulas (in a sense) on the sphere that are invariant under the transformations of the dihedral groups of rotations with inversion is described. This algorithm is applied for finding 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 April 23, 2021, published June 15, 2021

Language: English

DOI: 10.33048/semi.2021.18.050

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