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Siberian Journal of Numerical Mathematics

2017 year, number 4

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, pr. Acad. Lavrentieva 6, Novosibirsk, 630090, Russia
Keywords: численное интегрирование, инвариантные кубатурные формулы, инвариантные многочлены, группа вращений икосаэдра, numerical integration, invariant cubature formulas, invariant polynomials, icosahedral group of rotations

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 79th order of accuracy. The parameters of the new cubature formulas of the 21st, 25th and 29th orders of accuracy to 16 significant digits are given.