On optimal recovery in $L_2$
Numerical Analysis
2020-10-08 v1 Numerical Analysis
Functional Analysis
Abstract
We prove that the optimal error of recovery in the norm of functions from a class can be bounded above by the value of the Kolmogorov width of in the uniform norm. We demonstrate on a number of examples of from classes of functions with mixed smoothness that the obtained inequality provides a powerful tool for estimating errors of optimal recovery.
Keywords
Cite
@article{arxiv.2010.03103,
title = {On optimal recovery in $L_2$},
author = {V. Temlyakov},
journal= {arXiv preprint arXiv:2010.03103},
year = {2020}
}