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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2017, Volume 20, Number 4, Pages 413–423
DOI: https://doi.org/10.15372/SJNM20170405 (Mi sjvm660) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The cubature formulas on a sphere invariant to the icosahedral group of rotations with inversion

A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentiev av., Novosibirsk, 630090, Russia
Full-text PDF (435 kB) Citations (6)
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DOI: https://doi.org/10.15372/SJNM20170405
Abstract: An algorithm of the search for the best (in a sense) cubature formulas on a sphere that are invariant with respect to the transformations of the icosahedral group of rotations with inversion is described. This algorithm is applied to finding the parameters of all the best cubature formulas of this symmetry type up to the $79$th order of accuracy. The parameters of the new cubature formulas of the $21$st, $25$th and $29$th orders of accuracy to $16$ significant digits are given.
Key words: numerical integration, invariant cubature formulas, invariant polynomials, icosahedral group of rotations.
Received: 21.02.2017
Revised: 25.04.2017
English version:
Numerical Analysis and Applications, 2017, Volume 10, Issue 4, Pages 339–346
DOI: https://doi.org/10.1134/S199542391704005X
Bibliographic databases:
Document Type: Article
UDC: 519.644.7
Language: Russian
Citation: A. S. Popov, “The cubature formulas on a sphere invariant to the icosahedral group of rotations with inversion”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 413–423; Num. Anal. Appl., 10:4 (2017), 339–346
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
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