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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 9, Pages 1555–1565 (Mi zvmmf592)  

This article is cited in 2 scientific papers (total in 2 papers)

On the complexity and methods of polyhedral approximations of convex bodies with a partially smooth boundary

N. B. Brusnikina, G. K. Kamenev

Dorodnicyn Computational Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: Polyhedral approximation of nonsmooth convex compact bodies with a boundary having smooth portions of positive Gaussian curvature is considered. Examples of such bodies are reachable sets of dynamic control systems. The complexity of solving such approximation problems is estimated, and optimal approximation methods are discussed.

Key words: polyhedral approximations, convex bodies, partially smooth boundary, bound for complexity of approximation.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:9, 1500–1510

Bibliographic databases:
UDC: 519.651
Received: 11.10.2004

Citation: N. B. Brusnikina, G. K. Kamenev, “On the complexity and methods of polyhedral approximations of convex bodies with a partially smooth boundary”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1555–1565; Comput. Math. Math. Phys., 45:9 (2005), 1500–1510

Citation in format AMSBIB
\Bibitem{BruKam05}
\by N.~B.~Brusnikina, G.~K.~Kamenev
\paper On the complexity and methods of polyhedral approximations of convex bodies with a partially smooth boundary
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 9
\pages 1555--1565
\mathnet{http://mi.mathnet.ru/zvmmf592}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2216066}
\zmath{https://zbmath.org/?q=an:1087.52503}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 9
\pages 1500--1510


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. B. Brusnikina, A. V. Lotov, “Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions”, Comput. Math. Math. Phys., 47:11 (2007), 1779–1787  mathnet  crossref  mathscinet
    2. G. K. Kamenev, “Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies”, Comput. Math. Math. Phys., 48:3 (2008), 376–394  mathnet  crossref  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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