Geodesic
Weighted spherical semidesigns and cubature formulae for calculating integrals on a~sphere
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 49-55

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In this paper we study weighted spherical semidesigns, i.e., systems of points on a sphere of a specific type. We propose a new proof of the necessary and sufficient condition for a system of points on a sphere to be a weighted spherical semidesign. This criterion gives new approaches to the construction of cubature formulae for calculating integrals over a sphere with the degree of accuracy of 5 and 9.
Keywords: weighed spherical semidesign
Mots-clés : cubature formula. 
@article{IVM_2013_2_a4,
     author = {N. O. Kotelina and A. B. Pevnyi},
     title = {Weighted spherical semidesigns and cubature formulae for calculating integrals on a~sphere},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {49--55},
     publisher = {mathdoc},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_2_a4/}
}
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N. O. Kotelina; A. B. Pevnyi. Weighted spherical semidesigns and cubature formulae for calculating integrals on a~sphere. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2013), pp. 49-55. http://geodesic.mathdoc.fr/item/IVM_2013_2_a4/