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Matem. Mod., 2011, Volume 23, Number 2, Pages 3–26 (Mi mm3070)  

This article is cited in 4 scientific papers (total in 4 papers)

The quantitative conditionality criterium for the systems of linear algebraic equations

N. N. Kalitkin, L. F. Yukhno, L. V. Kuzmina

Keldysh Institute of Applied Mathematic, Moscow

Abstract: The well known conditionality criteria for systems of linear algebraic equation are shown to be unadecvate. The new criterium is propoused it is a quantitative, wich describes a loss of decimal digitals in computations. The adecvasy of this criterium is illustrated by numerical examples. The conditionality criteria are calculated for some important types of linear systems, arizing from difference schemes for differential or integral equations.

Keywords: systems of linear algebraic equations, conditionality criterium.

Full text: PDF file (524 kB)
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English version:
Mathematical Models and Computer Simulations, 2011, 3:5, 541–556

Bibliographic databases:

UDC: 519.612.2
Received: 28.06.2010

Citation: N. N. Kalitkin, L. F. Yukhno, L. V. Kuzmina, “The quantitative conditionality criterium for the systems of linear algebraic equations”, Matem. Mod., 23:2 (2011), 3–26; Math. Models Comput. Simul., 3:5 (2011), 541–556

Citation in format AMSBIB
\Bibitem{KalYukKuz11}
\by N.~N.~Kalitkin, L.~F.~Yukhno, L.~V.~Kuzmina
\paper The quantitative conditionality criterium for the systems of linear algebraic equations
\jour Matem. Mod.
\yr 2011
\vol 23
\issue 2
\pages 3--26
\mathnet{http://mi.mathnet.ru/mm3070}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2848796}
\transl
\jour Math. Models Comput. Simul.
\yr 2011
\vol 3
\issue 5
\pages 541--556
\crossref{https://doi.org/10.1134/S2070048211050097}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84887232623}


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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. N. N. Kalitkin, L. V. Kuzmina, “The improved form of the conjugated gradients method”, Math. Models Comput. Simul., 4:1 (2012), 68–81  mathnet  crossref  mathscinet
    2. N. N. Kalitkin, L. V. Kuzmina, “On the Craig method convergency for linear algebraic systems”, Math. Models Comput. Simul., 4:5 (2012), 509–526  mathnet  crossref  mathscinet  elib
    3. A. A. Belov, N. N. Kalitkin, “Evolyutsionnaya faktorizatsiya i sverkhbystryi schet na ustanovlenie”, Preprinty IPM im. M. V. Keldysha, 2013, 069, 36 pp.  mathnet
    4. A. A. Belov, N. N. Kalitkin, “Evolutional factorization and superfast relaxation count”, Math. Models Comput. Simul., 7:2 (2015), 103–116  mathnet  crossref
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