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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 389–396
DOI: https://doi.org/10.17377/semi.2018.15.035 (Mi semr926) 		 
This article is cited in 4 scientific papers (total in 4 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
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DOI: https://doi.org/10.17377/semi.2018.15.035
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.
Received February 2, 2018, published April 16, 2018
Bibliographic databases:
Document Type: Article
UDC: 519.644
MSC: 65D32
Language: Russian
Citation: A. S. Popov, “Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D}_{5d}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 389–396
Citation in format AMSBIB
\Bibitem{Pop18}
\by A.~S.~Popov
\paper Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D}_{5d}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 389--396
\mathnet{http://mi.mathnet.ru/semr926}
\crossref{https://doi.org/10.17377/semi.2018.15.035}
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