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Matematicheskoe modelirovanie, 2017, Volume 29, Number 5, Pages 96–108 (Mi mm3850)  
This article is cited in 2 scientific papers (total in 2 papers)

Application of the Richardson method in case of the unknown lower bound of a problem spectrum

M. V. Popovab, Yu. A. Poveschenkobc, V. A. Gasilovbc, A. V. Koldobad, T. S. Poveschenkoe

a École Normale Supérieure de Lyon, CRAL (UMR CNRS 5574), Université de Lyon 1, France
b Keldysh Institute of Applied Mathematics of RAS, Moscow
c National Research Nuclear University MEPhI, Moscow
d Moscow Institute of Physics and Technology, Dolgoprudnyy
e Kurchatov Institute of Atomic Energy, Moscow
Full-text PDF (349 kB) Citations (2)
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Abstract: An algorithm, which allows to use an iterative Richardson's method for solving a system of linear algebraic equations, with the matrix corresponding to a sign-definite self-adjoint operator, in case of the absence of information about the lower boundary of the spectrum of problem is presented. The algorithm is based on the simultaneous operation of the two competing processes, the effectiveness of which is constantly analyzed. The elements of linear algebra concerning the spectral estimates, which are necessary to understand the details of the Richardson method with Chebyshev set of parameters, are presented. The method is explained on the example of onedimensional equation of elliptic type.
Keywords: system of linear algebraic equations; matrix inversion; iterative methods; Richardson method.
Funding agency Grant number
Russian Science Foundation 16-11-00100
Russian Foundation for Basic Research 16-07-00519_а
16-29-15081_офи_м
Received: 19.07.2016
English version:
Mathematical Models and Computer Simulations, 2018, Volume 10, Issue 1, Pages 111–119
DOI: https://doi.org/10.1134/S2070048218010106
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Popov, Yu. A. Poveschenko, V. A. Gasilov, A. V. Koldoba, T. S. Poveschenko, “Application of the Richardson method in case of the unknown lower bound of a problem spectrum”, Matem. Mod., 29:5 (2017), 96–108; Math. Models Comput. Simul., 10:1 (2018), 111–119
Citation in format AMSBIB
\Bibitem{PopPovGas17}
\by M.~V.~Popov, Yu.~A.~Poveschenko, V.~A.~Gasilov, A.~V.~Koldoba, T.~S.~Poveschenko
\paper Application of the Richardson method in case of the unknown lower bound of a problem spectrum
\jour Matem. Mod.
\yr 2017
\vol 29
\issue 5
\pages 96--108
\mathnet{http://mi.mathnet.ru/mm3850}
\elib{https://elibrary.ru/item.asp?id=29255035}
\transl
\jour Math. Models Comput. Simul.
\yr 2018
\vol 10
\issue 1
\pages 111--119
\crossref{https://doi.org/10.1134/S2070048218010106}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042557383}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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