Geodesic
Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion~$\mathrm{D_{4h}}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 457-464

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An algorithm of searching for the best (in a sense) cubature formulas on a sphere that are invariant under the dihedral group of rotations with inversion $\mathrm{D_{4h}}$ is described. This algorithm is applied to find parameters of all the best cubature formulas of this symmetry group up to the 29th order of accuracy.
Keywords: numerical integration, dihedral group of rotations.
Mots-clés : invariant cubature formulas, invariant polynomials 
@article{SEMR_2015_12_a70,
     author = {A. S. Popov},
     title = {Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion~$\mathrm{D_{4h}}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {457--464},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a70/}
}
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A. S. Popov. Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion~$\mathrm{D_{4h}}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 457-464. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a70/