A. S. Popov, “The search for the best cubature formulae invariant under the octahedral group of rotations with inversion for a sphere”, Sib. Zh. Vychisl. Mat., 8:2 (2005), 143

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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2005, Volume 8, Number 2, Pages 143–148 (Mi sjvm216)

This article is cited in 11 scientific papers (total in 11 papers)

The search for the best cubature formulae invariant under the octahedral group of rotations with inversion for a sphere

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Full-text PDF (175 kB) Citations (11)

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Abstract: The definition of the best cubature formula invariant under the octahedral group of rotations with inversion for a sphere is given. The process of searching for the best cubature formulae of the given symmetry type is described. The table which contains the main characteristics of all the best today cubature formulae of the octahedral group of rotations with inversion up to the 53rd algebraic order of accuracy is given. The weights and the coordinates of the new cubature formulae of the 21st, 25th, 27th, 31st and 33rd orders of accuracy are given to 16 significant digits.

Key words: numerical integration, cubature formulae, octahedral group of rotations.

Received: 06.02.2003
Revised: 23.07.2004

Bibliographic databases:

UDC: 519.644.7

Language: Russian

Citation: A. S. Popov, “The search for the best cubature formulae invariant under the octahedral group of rotations with inversion for a sphere”, Sib. Zh. Vychisl. Mat., 8:2 (2005), 143–148

Citation in format AMSBIB

\Bibitem{Pop05}

\by A.~S.~Popov

\paper The search for the best cubature formulae invariant under the octahedral group of rotations with inversion for a~sphere

\jour Sib. Zh. Vychisl. Mat.

\yr 2005

\vol 8

\issue 2

\pages 143--148

\mathnet{http://mi.mathnet.ru/sjvm216}

\zmath{https://zbmath.org/?q=an:1112.65310}

Linking options:

https://www.mathnet.ru/eng/sjvm216

https://www.mathnet.ru/eng/sjvm/v8/i2/p143

This publication is cited in the following 11 articles:

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, “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
A. S. Popov, “Kubaturnye formuly na sfere, invariantnye otnositelno preobrazovanii gruppy vraschenii diedra s inversiei $D_{3d}$”, Sib. elektron. matem. izv., 16 (2019), 1196–1204
A. S. Popov, “Kubaturnye formuly na sfere, invariantnye otnositelno grupp simmetrii pravilnykh mnogogrannikov”, Sib. elektron. matem. izv., 14 (2017), 190–198
A. S. Popov, “The cubature formulas on a sphere invariant to the icosahedral group of rotations with inversion”, Num. Anal. Appl., 10:4 (2017), 339–346
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
A. S. Popov, “Kubaturnye formuly na sfere, invariantnye otnositelno gruppy tetraedra s inversiei”, Sib. elektron. matem. izv., 11 (2014), 372–379
A. S. Popov, “The cubature formulas on a sphere invariant with respect to a dihedral group of rotations with inversion $D_{6h}$”, Num. Anal. Appl., 6:1 (2013), 49–53
Malkov E.A., Ivanov M.S., “Ob odnoi skheme vychisleniya integrala stolknovenii boltsmana”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 13:1 (2012), 98–106 A scheme for evaluating the boltzmann collision integral
A. S. Popov, “The cubature formulas on a sphere that are invariant with respect to the icosahedral group of rotations”, Num. Anal. Appl., 1:4 (2008), 355–361

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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