This article is cited in 6 papers

Computational mathematics

Cubature formulas on a sphere invariant under the dihedral group D2h

A. S. Popov

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

Abstract: An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the transformations of dihedral group of rotations with inversion D2h is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry group 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 17, 2016, published March 25, 2016

DOI: 10.17377/semi.2016.13.018

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