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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 8, Pages 1388–1397
DOI: https://doi.org/10.31857/S0044466924080042 (Mi zvmmf11807) 		 
This article is cited in 1 scientific paper (total in 1 paper)

General numerical methods

Estimates of the $p$-norms of solutions and inverse matrices of systems of linear equations with a circulant matrix

Yu. S. Volkov, V. V. Bogdanov

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466924080042
Abstract: The article considers the problem of estimating solutions and inverse matrices of systems of linear equations with a circulant matrix in the $p$-norm, $1\le p<\infty$. An estimate for a diagonally dominant circulant matrix is obtained. Based on this result and the idea of decomposing a matrix into a product of matrices associated with the decomposition of a characteristic polynomial, an estimate for the general circulant matrix is proposed.
Key words: difference equation, circulant matrix, diagonal dominance, norm of the inverse matrix, solution estimate
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0015
This work was carried out as part of a state assignment for the Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences (project No. FWNF-2022-0015).
Received: 07.02.2024
Revised: 07.02.2024
Accepted: 02.05.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 8, Pages 1680–1688
DOI: https://doi.org/10.1134/S0965542524700908
Bibliographic databases:
Document Type: Article
UDC: 519.613
Language: Russian
Citation: Yu. S. Volkov, V. V. Bogdanov, “Estimates of the $p$-norms of solutions and inverse matrices of systems of linear equations with a circulant matrix”, Zh. Vychisl. Mat. Mat. Fiz., 64:8 (2024), 1388–1397; Comput. Math. Math. Phys., 64:8 (2024), 1680–1688
Citation in format AMSBIB
\Bibitem{VolBog24}
\by Yu.~S.~Volkov, V.~V.~Bogdanov
\paper Estimates of the $p$-norms of solutions and inverse matrices of systems of linear equations with a circulant matrix
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 8
\pages 1388--1397
\mathnet{http://mi.mathnet.ru/zvmmf11807}
\crossref{https://doi.org/10.31857/S0044466924080042}
\elib{https://elibrary.ru/item.asp?id=75224102}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 8
\pages 1680--1688
\crossref{https://doi.org/10.1134/S0965542524700908}
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  • https://www.mathnet.ru/eng/zvmmf11807
  • https://www.mathnet.ru/eng/zvmmf/v64/i8/p1388
    • This publication is cited in the following 1 articles:
    1. Yu. S. Volkov, “Estimates of the $ p $-Norms of Solutions to Difference Equations and Infinite Systems of Linear Equations”, Sib Math J, 65:6 (2024), 1327  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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