Affiliation:
1. College of Science, North China University of Technology, Beijing 100144, China
Abstract
In this article, we give the sharp bounds of probabilistic Kolmogorov N,δ-widths and probabilistic linear N,δ-widths of the multivariate Sobolev space W2A with common smoothness on a Sq norm equipped with the Gaussian measure μ, where A⊂Rd is a finite set. And we obtain the sharp bounds of average width from the results of the probabilistic widths. These results develop the theory of approximation of functions and play important roles in the research of related approximation algorithms for Sobolev spaces.
Funder
Capacity building for scientific and technological innovation services–basic scientific research business fees
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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