Asymptotic properties of the estimate refinement method in polyhedral approximation of multidimensional balls

DOI10.1134/S0965542515100115zbMath1347.65048MaRDI QIDQ904387

Georgy K. Kamenev

Publication date: 13 January 2016

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

polytopesHausdorff metricconvergence ratepolyhedral approximationcomputational geometryestimate refinement methodfacial structurenumber of verticesnumber of facesmultidimensional unit ball

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Approximation by convex sets (52A27) Hausdorff and packing measures (28A78)

Related Items (2)

Efficiency of the estimate refinement method for polyhedral approximation of multidimensional balls ⋮ Complexity of methods for approximating convex compact bodies by double description polytopes and complexity bounds for a hyperball

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A class of adaptive algorithms for approximating convex bodies by polyhedra
• Approximation of completely bounded sets by the deep holes method.
• Construction of suboptimal coverings of the multidimensional unit sphere
• Numerical analysis of the efficiency of an algorithm for approximating convex bodies by polyhedra
• Analysis of an algorithm for approximating convex bodies
• Interactive decision maps. Approximation and visualization of Pareto frontier
• The upper bound theorem for polytopes: An easy proof of its asymptotic version
• Polytopal approximation bounding the number of \(k\)-faces
• Approximating \(3\)-dimensional convex bodies by polytopes with a restricted number of edges
• Iterative method for constructing coverings of the multidimensional unit sphere
• Optimal growth order of the number of vertices and facets in the class of Hausdorff methods for polyhedral approximation of convex bodies
• Method for polyhedral approximation of a ball with an optimal order of growth of the facet structure cardinality
• The initial convergence rate of adaptive methods for polyhedral approximation of convex bodies
• Convex Polytopes
• The maximum numbers of faces of a convex polytope
• Efficient algorithms for approximation of nonsmooth convex bodies

This page was built for publication: Asymptotic properties of the estimate refinement method in polyhedral approximation of multidimensional balls