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

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2013, Volume 16, Number 1, Pages 57–62 (Mi sjvm498)

This article is cited in 9 scientific papers (total in 9 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

Full-text PDF (163 kB) Citations (9)

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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

English version:
Numerical Analysis and Applications, 2013, Volume 6, Issue 1, Pages 49–53
DOI: https://doi.org/10.1134/S1995423913010060

Bibliographic databases:

Document Type: Article

UDC: 519.644.7

Language: Russian

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

Citation in format AMSBIB

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\jour Num. Anal. Appl.

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Linking options:

https://www.mathnet.ru/eng/sjvm498

https://www.mathnet.ru/eng/sjvm/v16/i1/p57

This publication is cited in the following 9 articles:

A. S. Popov, “Cubature Formulas on the Sphere that are Invariant under Dihedral Rotation Groups”, Numer. Analys. Appl., 18:1 (2025), 78
A. S. Popov, “Poisk nailuchshikh kubaturnykh formul na sfere, invariantnykh otnositelno gruppy vraschenii ikosaedra”, Sib. zhurn. vychisl. matem., 26:4 (2023), 415–430
A. S. Popov, “Search for the Best Cubature Formulas on the Sphere Invariant under the Icosahedral Rotation Group”, Numer. Analys. Appl., 16:4 (2023), 348
Popov A.S., “Cubature Formulas on the Sphere That Are Invariant Under the Transformations of the Dihedral Groups of Rotations With Inversion”, Sib. Electron. Math. Rep., 18 (2021), 703–709
A. S. Popov, “Cubature formulas on the sphere that are invariant under the transformations of the dihedral group of rotations $D_4$ ”, Sib. elektron. matem. izv., 17 (2020), 964–970
Popov A.S., “Cubature Formulas on a Sphere That Are Invariant Under the Transformations of the Dihedral Group of Rotations With Inversion D-3D”, Sib. Electron. Math. Rep., 16 (2019), 1196–1204
A. S. Popov, “Kubaturnye formuly na sfere, invariantnye otnositelno gruppy vraschenii diedra s inversiei $\mathrm{D_{5d}}$ ”, Sib. elektron. matem. izv., 15 (2018), 389–396
A. S. Popov, “Kubaturnye formuly na sfere, invariantnye otnositelno gruppy diedra $\mathrm{D_{2h}}$ ”, Sib. elektron. matem. izv., 13 (2016), 252–259
A. S. Popov, “Kubaturnye formuly na sfere, invariantnye otnositelno gruppy vraschenii diedra s inversiei $\mathrm{D_{4h}}$ ”, Sib. elektron. matem. izv., 12 (2015), 457–464

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Sibirskii Zhurnal Vychislitel'noi Matematiki

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