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Matematicheskoe modelirovanie, 2015, Volume 27, Number 9, Pages 110–136 (Mi mm3652)  
This article is cited in 1 scientific paper (total in 1 paper)

Comparison of highly stable forms of iterative conjugate directions methods

A. A. Belovab, N. N. Kalitkinab, L. V. Kuzminaab

a Keldysh Institute of Applied Mathematics of RAS, Moscow
b Lomonosov Moscow State University, Faculty of Physics, Moscow
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Abstract: Simple and highly stable formulae for conjugate directions methods in case of symmetric matrices and for symmetrized conjugate gradients in case of non-symmetric matrices have been proposed. These methods are compared with highly stable forms of conjugate gradients method and Craig method. It is shown that recurrent algorithm versions are necessary for high round-off stability to be achieved. Conjugate residual method turned out to be the most reliable and fast for symmetric sign-definite and sign-alternating matrices. Symmetrized conjugate gradients method delivered the best results for non-symmetric matrices. These two methods are recommended for developing standard programs. Also a reliable criterion for breaking the count in case of reaching round-off background is constructed.
Keywords: systems of linear algebraic equations, sparse matrices, iterative methods, conjugate gradients descents.
Received: 24.06.2013
Revised: 07.04.2014
English version:
Mathematical Models and Computer Simulations, 2016, Volume 8, Issue 2, Pages 155–174
DOI: https://doi.org/10.1134/S2070048216020046
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Belov, N. N. Kalitkin, L. V. Kuzmina, “Comparison of highly stable forms of iterative conjugate directions methods”, Matem. Mod., 27:9 (2015), 110–136; Math. Models Comput. Simul., 8:2 (2016), 155–174
Citation in format AMSBIB
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\by A.~A.~Belov, N.~N.~Kalitkin, L.~V.~Kuzmina
\paper Comparison of highly stable forms of iterative conjugate directions methods
\jour Matem. Mod.
\yr 2015
\vol 27
\issue 9
\pages 110--136
\mathnet{http://mi.mathnet.ru/mm3652}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3545217}
\elib{https://elibrary.ru/item.asp?id=24850122}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 2
\pages 155--174
\crossref{https://doi.org/10.1134/S2070048216020046}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962711423}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математическое моделирование
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