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The initial convergence rate of adaptive methods for polyhedral approximation of convex bodies

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Abstract

The convergence rate at the initial stage is analyzed for a previously proposed class of asymptotically optimal adaptive methods for polyhedral approximation of convex bodies. Based on the results, the initial convergence rate of these methods can be evaluated for arbitrary bodies (including the case of polyhedral approximation of polytopes) and the resources sufficient for achieving optimal asymptotic properties can be estimated.

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Authors and Affiliations

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

    G. K. Kamenev

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  1. G. K. Kamenev
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Correspondence to G. K. Kamenev.

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Original Russian Text © G.K. Kamenev, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 5, pp. 763–778.

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Kamenev, G.K. The initial convergence rate of adaptive methods for polyhedral approximation of convex bodies. Comput. Math. and Math. Phys. 48, 724–738 (2008). https://doi.org/10.1134/S0965542508050035

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  • DOI: https://doi.org/10.1134/S0965542508050035

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