电邮这篇文章 A remark on constructive covering of a ball of finite dimensional Banach space
- 作者: Temlyakov V.N.1,2,3,4
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隶属关系:
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- Lomonosov Moscow State University, Moscow, Russia
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- University of South Carolina, Columbia, SC, USA
- 期: 卷 216, 编号 7 (2025)
- 页面: 96-108
- 栏目: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/306721
- DOI: https://doi.org/10.4213/sm10140
- ID: 306721
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详细
We discuss construction of coverings of the unit ball of a finite-dimensional Banach space. The well-known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of a good covering. Here we study incoherent systems and apply them to the construction of good coverings. We use the following strategy. First, we build a good covering by balls of radius close to one. Second, we iterate this construction to obtain a good covering for any radius. We provide a greedy-type algorithm for such constructions.
作者简介
Vladimir Temlyakov
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; Lomonosov Moscow State University, Moscow, Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia; University of South Carolina, Columbia, SC, USA
编辑信件的主要联系方式.
Email: temlyakovv@gmail.com
Doctor of physico-mathematical sciences, Professor
参考
- Е. Д. Глускин, “Октаэдр плохо приближается случайными подпространствами”, Функц. анализ и его прил., 20:1 (1986), 14–20
- Б. С. Кашин, Ю. В. Малыхин, К. С. Рютин, “Поперечник по Колмогорову и аппроксимативный ранг”, Гармонический анализ, теория приближений и теория чисел, Сборник статей. К 60-летию со дня рождения академика Сергея Владимировича Конягина, Труды МИАН, 303, МАИК “Наука/Интерпериодика”, М., 2018, 155–168
- V. N. Temlyakov, “Greedy approximations”, Foundations of computational mathematics (Santander, 2005), London Math. Soc. Lecture Note Ser., 331, Cambridge Univ. Press, Cambridge, 2006, 371–394
- V. Temlyakov, Greedy approximation, Cambridge Monogr. Appl. Comput. Math., 20, Cambridge Univ. Press, Cambridge, 2011, xiv+418 pp.
- В. Н. Темляков, “Некогерентные системы и покрытия в конечномерных банаховых пространствах”, Матем. сб., 205:5 (2014), 97–116
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