This article is cited in 5 papers

Computational mathematics

Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D}_{5d}$

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 D5d 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 2, 2018, published April 16, 2018

DOI: 10.17377/semi.2018.15.035

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