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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 1983, Volume 23, Number 1, Pages 213–216 (Mi zvmmf4544)  
Scientific communications

Duality relations connected with Gaussian elimination

Kh. D. Ikramov

Moscow
Full-text PDF (548 kB)
Abstract: Using the duality relations associated with Gauss's method it is shown that: 1. Any main submatrix of a totally non-degenerate matrix $A$; is stipulated (in the sense of an arbitrary monotonic norm) to be not inferior to $A$; itself; 2. If the inverse of matrix $A$; is diagonally dominant with respect to the columns, then the linear system $Ax=b$ is regularly solved by Jordan's method without the main element being chosen.
Received: 10.03.1981
English version:
USSR Computational Mathematics and Mathematical Physics, 1983, Volume 23, Issue 1, Pages 149–151
DOI: https://doi.org/10.1016/S0041-5553(83)80026-3
Bibliographic databases:
Document Type: Article
UDC: 519.612
Language: Russian
Citation: Kh. D. Ikramov, “Duality relations connected with Gaussian elimination”, Zh. Vychisl. Mat. Mat. Fiz., 23:1 (1983), 213–216; U.S.S.R. Comput. Math. Math. Phys., 23:1 (1983), 149–151
Citation in format AMSBIB
\Bibitem{Ikr83}
\by Kh.~D.~Ikramov
\paper Duality relations connected with Gaussian elimination
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 1983
\vol 23
\issue 1
\pages 213--216
\mathnet{http://mi.mathnet.ru/zvmmf4544}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=692757}
\transl
\jour U.S.S.R. Comput. Math. Math. Phys.
\yr 1983
\vol 23
\issue 1
\pages 149--151
\crossref{https://doi.org/10.1016/S0041-5553(83)80026-3}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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