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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 439, Pages 112–127 (Mi znsl6205)  
This article is cited in 24 scientific papers (total in 24 papers)

Problems of parallel solution of large systems of linear algebraic equations

V. P. Il'inab

a Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
Full-text PDF (227 kB) Citations (24)
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Abstract: The paper considers some modern problems arising in developing parallel algorithms for solving large systems of linear algebraic equations with sparse matrices occurring in mathematical modeling of real-life processes and phenomena on a multiprocessor computer system (MCS). Two main requirements to methods and technologies under consideration are fast convergence of iterations and scalable parallelism, which are intrinsically contradictory and need a special investigation. The paper analyzes main trends is developing preconditioned iterative methods in Krylov's subspaces based on algebraic domain decomposition and principles of their program implementation on a geterogeneous MCS with hierarchical memory structure.
Key words and phrases: system of linear algebraic equation, sparse matrix, iterative algorithm, preconditioning, Krylov subspaces, scalable parallelism, supercomputer, program library, component technologies.
Funding agency Grant number
Russian Science Foundation 14-11-00485
Russian Foundation for Basic Research 14-07-00128
Received: 23.10.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 216, Issue 6, Pages 795–804
DOI: https://doi.org/10.1007/s10958-016-2945-4
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: V. P. Il'in, “Problems of parallel solution of large systems of linear algebraic equations”, Computational methods and algorithms. Part XXVIII, Zap. Nauchn. Sem. POMI, 439, POMI, St. Petersburg, 2015, 112–127; J. Math. Sci. (N. Y.), 216:6 (2016), 795–804
Citation in format AMSBIB
\Bibitem{Ili15}
\by V.~P.~Il'in
\paper Problems of parallel solution of large systems of linear algebraic equations
\inbook Computational methods and algorithms. Part~XXVIII
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 439
\pages 112--127
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3502387}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 216
\issue 6
\pages 795--804
\crossref{https://doi.org/10.1007/s10958-016-2945-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84976324014}
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  • https://www.mathnet.ru/eng/znsl/v439/p112
    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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