On optimal recovery in L_2

Temlyakov V.

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On optimal recovery in L_2

机译：关于L_2的最佳恢复

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摘要

We prove that the optimal error of recovery in the L-2 norm of functions from a class F can be bounded above by the value of the Kolmogorov width of F in the uniform norm. We demonstrate on a number of examples of F from classes of functions with mixed smoothness that the obtained inequality provides a powerful tool for estimating errors of optimal recovery. (C) 2020 Elsevier Inc. All rights reserved.

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《Journal of complexity》 |2021年第8期|101545.1-101545.11|共11页
作者
Temlyakov V.;
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作者单位

Univ South Carolina Columbia SC 29208 USA|Steklov Inst Math Moscow Russia|Lomonosov Moscow State Univ Moscow Russia|Moscow Ctr Fundamental & Appl Math Moscow Russia;

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正文语种 eng
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关键词
Error of optimal recovery; Discretization; Least squares; Mixed smoothness;

机译：最佳恢复误差;离散化;最小二乘;混合平滑度;

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2. ON THE H_2, L_2, AND H_8,L_8 OPTIMALITY OF SOME TWO-DEGREE OF FREEDOM CONTROL SYSTEMS [J] . L. Keviczky, Cs. Banyasz Systems Science . 2007,第3期

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3. Stability and robustness of the l_2/l_q-minimization for block sparse recovery [J] . Yi Gao, Jigen Peng, Shigang Yue Signal processing . 2017,第Auga期

机译：块稀疏恢复的l_2 / l_q最小化的稳定性和鲁棒性
4. A Sublinear Algorithm for Sparse Reconstruction with l_2/l_2 Recovery Guarantees [C] . Robert Calderbank, Stephen Howard, Sina Jafarpour IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing . 2009

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On optimal recovery in L_2

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