The search of the best cubature formulas on the sphere that are invariant under the icosahedral rotation group
A.S. Popov
Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
Keywords: numerical integration, invariant cubature formulas, invariant polynomials, icosahedral rotation group
Abstract
A process of searching on the sphere for the best (in a sense) cubature formulas that are invariant under the transformations of the icosahedral rotation group is described. The parameters of the best cubature formulas of this symmetry type up to the 30th 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 icosahedral rotation group up to the 79th order of accuracy is given.
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