This article is cited in 7 scientific papers (total in 7 papers)
Iterative method for constructing coverings of the multidimensional unit sphere
G. K. Kameneva, A. V. Lotova, T. S. Mayskayab
a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
The stepwise-supplement-of-a-covering (SSC) method is described and examined. The method is intended for the numerical construction of near optimal coverings of the multidimensional unit sphere by neighborhoods of a finite number of points (covering basis). Coverings of the unit sphere are used, for example, in nonadaptive polyhedral approximation of multidimensional convex compact bodies based on the evaluation of their support function for directions defined by points of the covering basis. The SSC method is used to iteratively construct a sequence of coverings, each differing from the previous one by a single new point included in the covering basis. Although such coverings are not optimal, it is theoretically shown that they are asymptotically suboptimal. By applying an experimental analysis, the asymptotic efficiency of the SSC method is estimated and the method is shown to be relatively efficient for a small number of points in the covering basis.
methods for covering the multidimensional unit sphere, interactive method, stepwise-supplement-of-a-covering method, asymptotically suboptimal covering.
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Computational Mathematics and Mathematical Physics, 2013, 53:2, 131–143
G. K. Kamenev, A. V. Lotov, T. S. Mayskaya, “Iterative method for constructing coverings of the multidimensional unit sphere”, Zh. Vychisl. Mat. Mat. Fiz., 53:2 (2013), 181–194; Comput. Math. Math. Phys., 53:2 (2013), 131–143
Citation in format AMSBIB
\by G.~K.~Kamenev, A.~V.~Lotov, T.~S.~Mayskaya
\paper Iterative method for constructing coverings of the multidimensional unit sphere
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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A. V. Lotov, “Method for constructing an external polyhedral estimate of the trajectory tube for a nonlinear dynamic system”, Dokl. Math., 95:1 (2017), 95–98
G. K. Kamenev, A. V. Lotov, “Approximation of the effective hull of a nonconvex multidimensional set given by a nonlinear mapping”, Dokl. Math., 97:1 (2018), 104–108
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