NDLI: Nearly optimal coverings of a sphere with generalized spherical segments

Content Provider	Springer Nature Link
Author	Dulliev, A. M.
Copyright Year	2015
Abstract	The subject of this study is the incomplete covering of a two-dimensional sphere by sets resulting from the intersection of this sphere with a cone whose vertex is inside the sphere. A numerical method is proposed for evaluating the criterial function of the covering, which is representable in the form of a multiple minimax. The problem of optimally choosing the axes for the cones defining the sets in the covering is examined. By exploiting symmetry considerations, this problem is reduced to a similar problem of small dimension, which can be numerically treated on modern computers. The reduction is performed by solving an auxiliary optimization problem. It is shown that the criterial function of this problem is Lipschitzian. The results of several numerical tests are presented. For possible computer implementations of the proposed methods, certain recommendations on parallelizing some numerical procedures are given.
Starting Page	1110
Ending Page	1119
Page Count	10
File Format	PDF
ISSN	09655425
Journal	Computational Mathematics and Mathematical Physics
Volume Number	55
Issue Number	7
e-ISSN	15556662
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-07-26
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	incomplete coverings of spheres generalized spherical segment circular cone numerical method of optimization multiple minimax Computational Mathematics and Numerical Analysis
Content Type	Text
Resource Type	Article
Subject	Computational Mathematics

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