This article is cited in 3 papers

Computational mathematics

Cubature formulas on the sphere that are invariant under the transformations of the dihedral group of rotations $D_4$

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 group of rotations $D_4$ 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 February 27, 2020, published July 17, 2020

Language: English

DOI: 10.33048/semi.2020.17.071

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