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On optimal recovery in $L_2$

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arxiv 2010.03103 v1 pith:5CVXBDP2 submitted 2020-10-07 math.NA cs.NAmath.FA

V. Temlyakov This is my paper · ORCID
classification math.NAcs.NAmath.FA
keywords optimalrecoveryfunctionsnormaboveboundedclassclasses
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Some lower bounds for optimal sampling recovery of functions with mixed smoothness

    math.NA 2024-12 conditional novelty 6.0 of 10

    Optimal nonlinear sampling recovery of mixed-smoothness classes H^r_q is at least c m^{-r+1/q-1/p} (log m)^{(d-1)/p}, a logarithmic factor not captured by previous lower-bound techniques.

  2. Nonlinear approximation with adaptive dictionaries

    math.NA 2026-07 unverdicted novelty 5.0 of 10

    Sparse approximation of kernels with adaptive, kernel-dependent dictionaries controls sampling-recovery errors for families of integral-operator function classes.

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