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@article{SEMR_2016_13_a93, author = {A. S. Popov}, title = {Cubature formulas on a sphere invariant under the dihedral group {D2h}}, journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a}, pages = {252--259}, publisher = {mathdoc}, volume = {13}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a93/} }
A. S. Popov. Cubature formulas on a sphere invariant under the dihedral group D2h. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 252-259. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a93/
[1] S. L. Sobolev, “Cubature formulas on a sphere which are invariant under transformation of finite rotational groups”, Dokl. Akad. Nauk SSSR, 146:2 (1962), 310–313 (in Russian) | MR | Zbl
[2] S. L. Sobolev, “On mechanical cubature formulas for the surface of a sphere”, Sibirskii Mat. Zh., 3:5 (1962), 769–796 (in Russian) | MR | Zbl
[3] A. D. McLaren, “Optimal numerical integration on a sphere”, Math. Comput., 17:83 (1963), 361–383 | DOI | MR | Zbl
[4] V. I. Lebedev, “Nodes and weights of Gauss–Markov type quadrature formulas from 9th to 17th accuracy orders for a sphere which are invariant under the octahedral group with inversion”, Zh. Vychisl. Mat. Mat. Fiz., 15:1 (1975), 48–54 (in Russian) | MR | Zbl
[5] V. I. Lebedev, “On quadratures for a sphere”, Zh. Vychisl. Mat. Mat. Fiz., 16:2 (1976), 293–306 (in Russian) | MR | Zbl | Zbl
[6] V. I. Lebedev, “Quadrature formulas for a sphere of the 25th to the 29th orders of accuracy”, Sibirskii Mat. Zh., 18:1 (1977), 132–142 (in Russian) | MR | Zbl
[7] V. I. Lebedev, D. N. Laikov, “Quadrature formula of 131st algebraic order of accuracy for a sphere”, Dokl. RAN, 366:6 (1999), 741–745 (in Russian) | MR | Zbl
[8] S. I. Konyaev, “Gauss type quadratures for a sphere invariant under icosahedral group with inversion”, Mat. Zametki, 25:4 (1979), 629–634 (in Russian) | MR | Zbl
[9] S. I. Konyaev, “Formulas for numerical integration on a sphere”, Embedding Theorems and Their Applications, Trudy Seminara Akad. S. L. Soboleva, 1, Novosibirsk, 1982, 75–82 (in Russian) | MR | Zbl
[10] S. I. Konyaev, “On invariant quadrature formulae for a sphere”, Russ. J. Numer. Anal. Math. Modelling, 10:1 (1995), 41–47 | DOI | MR | Zbl
[11] I. P. Mysovskikh, Interpolation Cubature Formulas, Nauka, M., 1981 (in Russian) | MR | Zbl
[12] A. S. Popov, “Cubature formulae for a sphere which are invariant with respect to the tetrahedral group”, Computational Mathematics and Mathematical Physics, 35:3 (1995), 369–374 | MR | Zbl
[13] A. S. Popov, “Cubature formulae of high orders of accuracy for a sphere which are invariant with respect to the tetrahedral group”, Computational Mathematics and Mathematical Physics, 36:4 (1996), 417–421 | MR | Zbl
[14] A. S. Popov, “Cubature formulas on a sphere that are invariant with respect to octahedron rotation groups”, Computational Mathematics and Mathematical Physics, 38:1 (1998), 30–37 | MR | Zbl
[15] A. S. Popov, “The search for the sphere of the best cubature formulae invariant under octahedral group of rotations”, Siberian J. of Numer. Mathematics, 5:4 (2002), 367–372 (in Russian)
[16] A. S. Popov, “The search for the best cubature formulae invariant under the octahedral group of rotations with inversion for a sphere”, Siberian J. of Numer. Mathematics, 8:2 (2005), 143–148 (in Russian) | Zbl
[17] A. S. Popov, “Cubature formulas on a sphere invariant under the icosahedral rotation group”, Numerical Analysis and Applications, 1:4 (2008), 355–361 | DOI
[18] A. S. Popov, “Cubature formulas on a sphere invariant under the tetrahedral group with inversion”, Siberian Electronic Mathematical Reports, 11 (2014), 372–379 (in Russian) | Zbl
[19] A. S. Popov, “Cubature formulae of the fourth and seventh accuracy orders for a sphere invariant under the group of rotations of a square about the polar axis”, Numerical Methods and Techniques of Solving Problems in Mathematical Physics, Comp. Cent., Sib. Branch, Russian Acad. Sci., Novosibirsk, 1993, 47–53 (in Russian) | MR
[20] A. S. Popov, “Cubature formulae for a sphere invariant under cyclic rotation groups”, Russ. J. Numer. Anal. Math. Modelling, 9:6 (1994), 535–546 | DOI | MR | Zbl
[21] A. S. Popov, “Cubature formulas on a sphere that are invariant with respect to a group of dihedron rotations with inversion D6h”, Numerical Analysis and Applications, 6:1 (2013), 49–53 | DOI | Zbl
[22] A. S. Popov, “Cubature formulas on a sphere invariant under the dihedral group of rotations with inversion D4h”, Siberian Electronic Mathematical Reports, 12 (2015), 457–464 (in Russian)
[23] A. N. Kazakov, V. I. Lebedev, “Gauss type quadrature formulas for a sphere that are invariant with respect to the group of dihedron”, Trudy Math. Inst. RAN, 203, Nauka, M., 1994, 100–112 (in Russian) | MR | Zbl
[24] F. Klein, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, Dover, New York, 1956 | MR | Zbl
[25] L. D. Landau, E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Nauka, M., 1989 (in Russian) | Zbl
[26] V. A. Ditkin, “On some approximate formulas for calculating triple integrals”, Dokl. Akad. Nauk SSSR, 62:4 (1948), 445–447 (in Russian) | MR | Zbl
[27] V. A. Ditkin, L. A. Lyusternik, “On a method of practical harmonic analysis on a sphere”, Vychisl. Matematika i Vychisl. Tekhnika, 1, Mashgiz, M., 1953, 3–13 (in Russian) | MR | Zbl