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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2012, Volume 52, Number 5, Pages 818–828
(Mi zvmmf9711)
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This article is cited in 4 scientific papers (total in 4 papers)
Polyhedral approximation of convex compact bodies by filling methods
G. K. Kameneva, A. I. Pospelovb a Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
b A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow
Abstract:
A class of iterative methods – filling methods – for polyhedral approximation of convex compact bodies is introduced and studied. In contrast to augmentation methods, the vertices of the approximating polytope can lie not only on the boundary of the body but also inside it. Within the proposed class, Hausdorff or $H$-methods of filling are singled out, for which the convergence rates (asymptotic and at the initial stage of the approximation) are estimated. For the approximation of nonsmooth convex compact bodies, the resulting convergence rate estimates coincide with those for augmentation $H$-methods.
Key words:
convex sets, polytopes, iterative algorithms, polyhedral approximation, convergence rate of an algorithm.
Received: 04.05.2011 Revised: 27.11.2011
Citation:
G. K. Kamenev, A. I. Pospelov, “Polyhedral approximation of convex compact bodies by filling methods”, Zh. Vychisl. Mat. Mat. Fiz., 52:5 (2012), 818–828; Comput. Math. Math. Phys., 52:5 (2012), 680–690
Linking options:
https://www.mathnet.ru/eng/zvmmf9711 https://www.mathnet.ru/eng/zvmmf/v52/i5/p818
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Abstract page: | 276 | Full-text PDF : | 93 | References: | 51 | First page: | 18 |
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