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This article is cited in 2 scientific papers (total in 2 papers)
Distribution of the points of a design on the sphere
V. A. Yudin
Moscow Power Engineering Institute (Technical University)
Abstract:
We determine the size of spherical caps with centres at the points of a design that cover the whole sphere in Euclidean space with a given multiplicity. By projecting $q$-designs on one-dimensional subspaces, we obtain the nodes of a Chebyshev-type quadrature formula of the same precision $q$. For large values of $q$ we establish that the points of a minimal
$q$-design are uniformly distributed on the sphere. We construct a weighted cubature formula on the sphere with the minimum number of nodes.
DOI:
https://doi.org/10.4213/im661
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English version:
Izvestiya: Mathematics, 2005, 69:5, 1061–1079
Bibliographic databases:
    
UDC:
517.5
MSC: 05B30, 65D32, 05B40, 05E35, 33C45
Received: 27.11.2003
Citation:
V. A. Yudin, “Distribution of the points of a design on the sphere”, Izv. RAN. Ser. Mat., 69:5 (2005), 205–224; Izv. Math., 69:5 (2005), 1061–1079
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http://mi.mathnet.ru/eng/izv661https://doi.org/10.4213/im661 http://mi.mathnet.ru/eng/izv/v69/i5/p205
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This publication is cited in the following articles:
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Bannai Eiichi, Bannai Etsuko, “A survey on spherical designs and algebraic combinatorics on spheres”, European J. Combin., 30:6 (2009), 1392–1425
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A. R. Alimov, I. G. Tsar'kov, “Chebyshev centres, Jung constants, and their applications”, Russian Math. Surveys, 74:5 (2019), 775–849
 
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