Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2020, Volume 23, Number 3, Pages 315–324
DOI: https://doi.org/10.15372/SJNM20200306 (Mi sjvm750) 		 
Orthogonal projectors and systems of linear algebraic equations

I. V. Kireev

Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44, Krasnoyarsk, 660036 Russia
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DOI: https://doi.org/10.15372/SJNM20200306
Abstract: In this paper, an operator iterative procedure for constructing of the orthogonal projection of a vector on a given subspace is proposed. The algorithm is based on the Euclidean ortogonalization of power sequences of a special linear transformation generated by the original subspace. For consistent systems of linear algebraic equations, a numerical method based on this idea is proposed. Numerical results are presented.
Key words: numerical methods, linear algebra, orthogonal projectors, Kaczmarz method, Krylov subspaces.
Received: 19.02.2019
Revised: 31.01.2020
Accepted: 16.04.2020
English version:
Numerical Analysis and Applications, 2020, Volume 13, Issue 3, Pages 262–270
DOI: https://doi.org/10.1134/S1995423920030064
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: I. V. Kireev, “Orthogonal projectors and systems of linear algebraic equations”, Sib. Zh. Vychisl. Mat., 23:3 (2020), 315–324; Num. Anal. Appl., 13:3 (2020), 262–270
Citation in format AMSBIB
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\by I.~V.~Kireev
\paper Orthogonal projectors and systems of linear algebraic equations
\jour Sib. Zh. Vychisl. Mat.
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\vol 23
\issue 3
\pages 315--324
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\crossref{https://doi.org/10.15372/SJNM20200306}
\transl
\jour Num. Anal. Appl.
\yr 2020
\vol 13
\issue 3
\pages 262--270
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