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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2025, Volume 28, Number 1, Pages 89–99
DOI: https://doi.org/10.15372/SJNM20250107 (Mi sjvm896) 		 
Cubature formulas on the sphere that are invariant under dihedral rotation groups

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.15372/SJNM20250107
Abstract: A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of different dihedral rotation groups is described. The parameters of the new cubature formulas of the 6th, 10th, and 12th order of accuracy are given to 16 significant digits. A table which contains the main characteristics of all the best to date cubature formulas of the dihedral rotation group up to the 29th order of accuracy is given.
Key words: numerical integration, invariant cubature formulas, invariant polynomials, dihedral rotation group.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNM-2022-0001
This work was supported by Institute of Computational Mathematics and Mathematical Geophysics SB RAS under state contract FWNM-2022-0001.
Received: 10.04.2024
Revised: 25.04.2024
Accepted: 20.09.2024
English version:
Numerical Analysis and Applications, 2025, Volume 18, Issue 1, Pages 78–85
DOI: https://doi.org/10.1134/S1995423925010070
Bibliographic databases:
Document Type: Article
UDC: 519.644.7
Language: Russian
Citation: A. S. Popov, “Cubature formulas on the sphere that are invariant under dihedral rotation groups”, Sib. Zh. Vychisl. Mat., 28:1 (2025), 89–99; Num. Anal. Appl., 18:1 (2025), 78–85
Citation in format AMSBIB
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\by A.~S.~Popov
\paper Cubature formulas on the sphere that are invariant under dihedral rotation groups
\jour Sib. Zh. Vychisl. Mat.
\yr 2025
\vol 28
\issue 1
\pages 89--99
\mathnet{http://mi.mathnet.ru/sjvm896}
\crossref{https://doi.org/10.15372/SJNM20250107}
\edn{https://elibrary.ru/IDEVQQ}
\transl
\jour Num. Anal. Appl.
\yr 2025
\vol 18
\issue 1
\pages 78--85
\crossref{https://doi.org/10.1134/S1995423925010070}
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