Geodesic
Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D}_{5d}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 389-396

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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 dihedral group of rotations with inversion D5d is described. This algorithm is applied to find the parameters of all the best cubature formulas of this symmetry type up to the 35th order of accuracy.
Keywords: numerical integration, dihedral group of rotations.
Mots-clés : invariant cubature formulas, invariant polynomials 
@article{SEMR_2018_15_a112,
     author = {A. S. Popov},
     title = {Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D}_{5d}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {389--396},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a112/}
}
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A. S. Popov. Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion $\mathrm{D}_{5d}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 389-396. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a112/