This article is cited in 1 paper

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

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.

Key words: numerical integration, invariant cubature formulas, invariant polynomials, icosahedral rotation group.

UDC: 519.644.7

Received: 12.05.2023
Revised: 06.06.2023
Accepted: 05.09.2023

DOI: 10.15372/SJNM20230406

 English version: Numerical Analysis and Applications, 2023, 16:4, 348–358