On optimal recovery in L₂

2020/10/07 by Temlyakov, V. · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2010.03103

Abstract

We prove that the optimal error of recovery in the L₂ 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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• Sampling and entropy numbers in the uniform norm
• Sparse grids vs. random points for high-dimensional polynomial approximation

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