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On optimal recovery in $L_2$
Published 7 Oct 2020 in math.NA, cs.NA, and math.FA | (2010.03103v1)
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.
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