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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 190–198
DOI: https://doi.org/10.17377/semi.2017.14.019 (Mi semr778) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Computational mathematics

Cubature formulas on a sphere invariant under the symmetry groups of regular polyhedrons

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Akad. Lavrent'eva, 6, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2017.14.019
Abstract: An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the transformations of the symmetry groups of regular polyhedrons is described. This algorithm is applied to find 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, symmetry groups, rotation groups, regular polyhedrons.
Received January 27, 2017, published March 9, 2017
Document Type: Article
UDC: 519.644
MSC: 65D32
Language: Russian
Citation: A. S. Popov, “Cubature formulas on a sphere invariant under the symmetry groups of regular polyhedrons”, Sib. Èlektron. Mat. Izv., 14 (2017), 190–198
Citation in format AMSBIB
\Bibitem{Pop17}
\by A.~S.~Popov
\paper Cubature formulas on a sphere invariant under the symmetry groups of regular polyhedrons
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 190--198
\mathnet{http://mi.mathnet.ru/semr778}
\crossref{https://doi.org/10.17377/semi.2017.14.019}
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