Year: 2020
Type: preprint
Abstract: We prove that the optimal error of recovery in the $L_2$ norm of functions from a class $\bF$ can be bounded above by the value of the Kolmogorov width of $\bF$ in the uniform norm. We demonstrate on a number of examples of $\bF$ from classes of functions with mixed smoothness that the obtained inequality provides a powerful tool for estimating errors of optimal recovery.
Source: arXiv (Cornell University)
Author: Temlyakov, V.
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3092368447