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Matem. Mod., 2004, Volume 16, Number 7, Pages 13–20 (Mi mm251)  

This article is cited in 3 scientific papers (total in 3 papers)

On a solving ill-conditioned linear systems by iterative methods

A. S. Pavlova, L. F. Yukhnob

a M. V. Lomonosov Moscow State University
b Institute for Mathematical Modelling, Russian Academy of Sciences

Abstract: The question of application of iterative conjugate gradients methods to solve ill-conditioned linear algebraic equations is discussed in this work. It is shown that for the arbitrary decisions these methods do not improve the precision in comparison with direct methods. Nevertheless for one main class that imitated non-orthogonal system expansion of function the concerned methods may get 5-6$^{\mathrm{th}}$ order of accuracy while direct ones can't get at least 1$^{\mathrm{th}}$.

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Received: 10.11.2003

Citation: A. S. Pavlov, L. F. Yukhno, “On a solving ill-conditioned linear systems by iterative methods”, Matem. Mod., 16:7 (2004), 13–20

Citation in format AMSBIB
\Bibitem{PavYuk04}
\by A.~S.~Pavlov, L.~F.~Yukhno
\paper On a solving ill-conditioned linear systems by iterative methods
\jour Matem. Mod.
\yr 2004
\vol 16
\issue 7
\pages 13--20
\mathnet{http://mi.mathnet.ru/mm251}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2101689}
\zmath{https://zbmath.org/?q=an:1058.65043}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. F. Yukhno, “A modification of conjugate direction methods”, Comput. Math. Math. Phys., 46:1 (2006), 5–9  mathnet  crossref  mathscinet  zmath
    2. L. F. Yukhno, “On modification of certain methods of the conjugate direction type for solving systems of linear algebraic equations”, Comput. Math. Math. Phys., 47:11 (2007), 1737–1744  mathnet  crossref  mathscinet
    3. E. A. Vedutenko, S. V. Talalov, “About calculation of unperturbative amplitude for the scattering of the quantum particle on a complicated object”, Math. Models Comput. Simul., 2:5 (2010), 597–604  mathnet  crossref
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