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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 11, Page 1816
DOI: https://doi.org/10.31857/S0044466923110248 (Mi zvmmf11645) 		 
General numerical methods

Lower bounds for column matrix approximations

A. I. Osinsky

Institute of Numerical Mathematics, RAS, 119991 Moscow, RAS, Gubkina Street, 8, Russia
DOI: https://doi.org/10.31857/S0044466923110248
Abstract: We show a connection between lower and upper bounds on the column matrix approximation accuracy and the bounds on the norms of the pseudoinverses of the submatrices of orthogonal matrices. This connection is exploited to derive lower bounds for column approximations accuracy in spectral and Frobenius norms.
Key words: low-rank approximation, column subset selection, well-conditioned submatrices.
Received: 20.06.2023
Revised: 20.06.2023
Accepted: 25.07.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 11, Pages 2024–2037
DOI: https://doi.org/10.1134/S0965542523110167
Bibliographic databases:
Document Type: Article
UDC: 512.643
Language: English
Citation: A. I. Osinsky, “Lower bounds for column matrix approximations”, Zh. Vychisl. Mat. Mat. Fiz., 63:11 (2023), 1816; Comput. Math. Math. Phys., 63:11 (2023), 2024–2037
Citation in format AMSBIB
\Bibitem{Osi23}
\by A.~I.~Osinsky
\paper Lower bounds for column matrix approximations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 11
\pages 1816
\mathnet{http://mi.mathnet.ru/zvmmf11645}
\crossref{https://doi.org/10.31857/S0044466923110248}
\elib{https://elibrary.ru/item.asp?id=54720588}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 11
\pages 2024--2037
\crossref{https://doi.org/10.1134/S0965542523110167}
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