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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 389–396 (Mi semr926)

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.

DOI: https://doi.org/10.17377/semi.2018.15.035

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Bibliographic databases:

Document Type: Article
UDC: 519.644
MSC: 65D32
Received February 2, 2018, published April 16, 2018

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} `