Efficiency of the estimate refinement method for polyhedral approximation of multidimensional balls

DOI10.1134/S0965542516050080zbMath1356.65037MaRDI QIDQ327054

Georgy K. Kamenev

Publication date: 13 October 2016

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

zbMATH Keywords

numerical examplesconvergence ratepolyhedral approximationconvex bodiesestimate refinement methodestimate of algorithmsfacial structuremultidimensional balloptimal method

Mathematics Subject Classification ID

Algorithms for approximation of functions (65D15)

Related Items (3)

Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics ⋮ Finding sets of solutions to systems of nonlinear inequalities ⋮ Approximating a solution set of nonlinear inequalities

Cites Work

• Asymptotic properties of the estimate refinement method in polyhedral approximation of multidimensional balls
• 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
• Methods and algorithms for analyzing linear systems, by constructing generalized sets of attainability
• Efficient algorithms for approximation of nonsmooth convex bodies
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