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
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.
polyhedral approximations, convex bodies, partially smooth boundary, bound for complexity of approximation.
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Computational Mathematics and Mathematical Physics, 2005, 45:9, 1500–1510
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
\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.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
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
G. K. Kamenev, “Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies”, Comput. Math. Math. Phys., 48:3 (2008), 376–394
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