Email this article Some lower bounds for optimal sampling recovery of functions with mixed smoothness
- Authors: Gasnikov A.V.1,2,3, Temlyakov V.N.4,2,5,6
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Affiliations:
- Ivannikov Institute for System Programming of the Russian Academy of Science, Moscow, Russia
- Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
- Innopolis University, Innopolis, Russia
- University of South Carolina, Columbia, SC, USA
- Lomonosov Moscow State University, Moscow, Russia
- Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
- Issue: Vol 216, No 11 (2025)
- Pages: 90-107
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/351336
- DOI: https://doi.org/10.4213/sm10250
- ID: 351336
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Abstract
Recently there was a substantial progress in the problem of sampling recovery on function classes with mixed smoothness. It was mostly done by proving new and sometimes optimal upper bounds for both linear sampling recovery and nonlinear sampling recovery. In this paper we address the problem of lower bounds for the optimal rates of nonlinear sampling recovery. In the case of linear recovery one can use the well-developed theory of estimating the Kolmogorov and linear widths to establish some lower bounds for the optimal rates. In the case of nonlinear recovery we cannot use the above approach. It seems like the only technique which is available now is based on some simple observations. We demonstrate how these observations can be used.
Keywords
About the authors
Alexander Vladimirovich Gasnikov
Ivannikov Institute for System Programming of the Russian Academy of Science, Moscow, Russia; Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; Innopolis University, Innopolis, Russia
Email: gasnikov@yandex.ru
ORCID iD: 0000-0002-7386-039X
Scopus Author ID: 15762551000
ResearcherId: L-6371-2013
Doctor of physico-mathematical sciences, Associate professor
Vladimir Nikolaevich Temlyakov
University of South Carolina, Columbia, SC, USA; Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; Lomonosov Moscow State University, Moscow, Russia; Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
Email: temlyakovv@gmail.com
Doctor of physico-mathematical sciences, Professor
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