Geodesic
Cubature formulas on~the~sphere that are invariant under~the~transformations of~the~dihedral group of~rotations~$D_4$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 964-970

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An algorithm for finding the best cubature formulas (in a sense) on the sphere that are invariant under the transformations of the dihedral group of rotations $D_4$ is described. This algorithm is applied for finding 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_2020_17_a119,
     author = {A. S. Popov},
     title = {Cubature formulas on~the~sphere that are invariant under~the~transformations of~the~dihedral group of~rotations~$D_4$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {964--970},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a119/}
}
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A. S. Popov. Cubature formulas on~the~sphere that are invariant under~the~transformations of~the~dihedral group of~rotations~$D_4$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 964-970. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a119/