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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2013, Volume 16, Number 1, Pages 57–62
(Mi sjvm498)
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This article is cited in 8 scientific papers (total in 8 papers)
The cubature formulas on a sphere invariant with respect to a dihedral group of rotations with inversion $D_{6h}$
A. S. Popov Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant with respect to a dihedral group of rotations with inversion D6h has been veloped. This algorithm was applied to find parameters of all the best cubature formulas of this group of symmetry up to the $23$rd order of accuracy $n$. In the course of the study carried out, the exact values of parameters of the corresponding cubature formulas were found for $n\le11$, and the approximate ones were obtained by the numerical solution of systems of nonlinear algebraic equations by a Newton-type method for the other $n$. For the first time, the ways of obtaining the best cubature formulas for the sphere were systematically investigated for the case of the group which is not a subgroup of the groups of symmetry of the regular polyhedrons.
Key words:
numerical integration, invariant cubature formulas, invariant polynomials, dihedral group of rotations.
Received: 01.09.2011
Citation:
A. S. Popov, “The cubature formulas on a sphere invariant with respect to a dihedral group of rotations with inversion $D_{6h}$”, Sib. Zh. Vychisl. Mat., 16:1 (2013), 57–62; Num. Anal. Appl., 6:1 (2013), 49–53
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https://www.mathnet.ru/eng/sjvm498 https://www.mathnet.ru/eng/sjvm/v16/i1/p57
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Abstract page: | 318 | Full-text PDF : | 87 | References: | 47 | First page: | 7 |
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