Geodesic
Cubature formulas on a sphere invariant under the symmetry groups of regular polyhedrons
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 190-198

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An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the transformations of the symmetry groups of regular polyhedrons is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry type up to the 35th order of accuracy.
Keywords: numerical integration, symmetry groups, rotation groups, regular polyhedrons.
Mots-clés : invariant cubature formulas, invariant polynomials 
@article{SEMR_2017_14_a103,
     author = {A. S. Popov},
     title = {Cubature formulas on a sphere invariant under the symmetry groups of regular polyhedrons},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {190--198},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a103/}
}
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A. S. Popov. Cubature formulas on a sphere invariant under the symmetry groups of regular polyhedrons. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 190-198. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a103/