English

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 L2L_2 norm of functions from a class \bF\bF can be bounded above by the value of the Kolmogorov width of \bF\bF in the uniform norm. We demonstrate on a number of examples of \bF\bF 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}
}
R2 v1 2026-06-23T19:06:36.608Z