Author:
Tan Xin,Wang Yanan,Sun Lu,Shao Xingfeng,Chen Guanggui
Abstract
AbstractIn this article, we first put forward a new definition of probabilistic Gel’fand-$(N,\delta )$(N,δ)-width which is the classical Gel’fand-N-width in a probabilistic setting. Then we estimate the sharp order of the probabilistic Gel’fand-$(N,\delta )$(N,δ)-width of finite-dimensional space. Furthermore, we obtain the exact order of probabilistic Gel’fand-$(N, \delta )$(N,δ)-width of univariate Sobolev space by the discretization method according to the result of finite-dimensional space.
Funder
Innovation fund of Xihua university
Natural Science Foundation of China
the Key scientific research fund of Xihua University
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
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