A. S. Popov, “Cubature formulas on a sphere invariant under the tetrahedral group with inversion”, Sib. Èlektron. Mat. Izv., 2014, Volume 11,Pages <nobr>372

This article is cited in 5 papers

Computational mathematics

Cubature formulas on a sphere invariant under the tetrahedral group with inversion

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The unified algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the tetrahedral group of rotations with inversion is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry group up to the 41st order of accuracy.

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

UDC: 519.644

MSC: 65D32

Received February 17, 2014, published May 26, 2014