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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
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
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
Linking options:
https://www.mathnet.ru/eng/sjvm660 https://www.mathnet.ru/eng/sjvm/v20/i4/p413
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Abstract page: | 218 | Full-text PDF : | 35 | References: | 24 | First page: | 8 |
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