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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 5, Pages 763–778 (Mi zvmmf135)  

This article is cited in 7 scientific papers (total in 7 papers)

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

G. K. Kamenev

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

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.

Key words: convex body, polyhedral approximation, algorithm, approximation method, complexity bound.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:5, 724–738

Bibliographic databases:

UDC: 519.651
Received: 02.07.2007

Citation: G. K. Kamenev, “The initial convergence rate of adaptive methods for polyhedral approximation of convex bodies”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008), 763–778; Comput. Math. Math. Phys., 48:5 (2008), 724–738

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. I. Dudov, E. A. Mescheryakova, “O priblizhennom reshenii zadachi ob asferichnosti vypuklogo kompakta”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 10:4 (2010), 13–17  mathnet  crossref  elib
    2. S. I. Dudov, E. A. Mescheryakova, “Kharakterizatsiya ustoichivosti resheniya zadachi ob asferichnosti vypuklogo kompakta”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 11:2 (2011), 20–26  mathnet  crossref  elib
    3. S. I. Dudov, E. A. Meshcheryakova, “Method for finding an approximate solution of the asphericity problem for a convex body”, Comput. Math. Math. Phys., 53:10 (2013), 1483–1493  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. S. I. Dudov, E. A. Meshcheryakova, “On asphericity of convex body”, Russian Math. (Iz. VUZ), 59:2 (2015), 36–47  mathnet  crossref
    5. S. I. Dudov, “Systematization of problems on ball estimates of a convex compactum”, Sb. Math., 206:9 (2015), 1260–1280  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. G. K. Kamenev, “Asymptotic properties of the estimate refinement method in polyhedral approximation of multidimensional balls”, Comput. Math. Math. Phys., 55:10 (2015), 1619–1632  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. G. K. Kamenev, “Efficiency of the estimate refinement method for polyhedral approximation of multidimensional balls”, Comput. Math. Math. Phys., 56:5 (2016), 744–755  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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