On polyhedral approximations in an n-dimensional space

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• 作者：M. V. Balashov
• 关键词：modulus of continuity ; Hausdorff metric ; supporting function ; grid ; polyhedral approximation in Rn
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：56
• 期：10
• 页码：1679-1685
• 全文大小：248 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1555-6662
• 卷排序：56

文摘

The polyhedral approximation of a positively homogeneous (and, in general, nonconvex) function on a unit sphere is investigated. Such a function is presupporting (i.e., its convex hull is the supporting function) for a convex compact subset of Rn. The considered polyhedral approximation of this function provides a polyhedral approximation of this convex compact set. The best possible estimate for the error of the considered approximation is obtained in terms of the modulus of uniform continuous subdifferentiability in the class of a priori grids of given step in the Hausdorff metric.