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Diskr. Mat., 2008, Volume 20, Issue 1, Pages 145–150 (Mi dm997)  

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

A block algorithm of Lanczos type for solving sparse systems of linear equations

M. A. Cherepnev


Abstract: We suggest a new block algorithm for solving sparse systems of linear equations over $GF(2)$ of the form $Ax=b$, $A\in F(N\times N)$, $b\in F(N\times1)$, where $A$ is a symmetric matrix, $F=GF(2)$ is a field with two elements. The algorithm is constructed with the use of matrix Padé approximations. The running time of the algorithm with the use of parallel calculations is $\max\{O(dN^2/n),O(N^2)\}$, where $d$ is the maximal number of nonzero elements over all rows of the matrix $A$. If $d<Cn$ for some absolute constant $C$, then this estimate is better than the estimate of the running time of the well-known Montgomery algorithm.

DOI: https://doi.org/10.4213/dm997

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English version:
Discrete Mathematics and Applications, 2008, 18:1, 79–84

Bibliographic databases:

UDC: 519.7
Received: 18.04.2007

Citation: M. A. Cherepnev, “A block algorithm of Lanczos type for solving sparse systems of linear equations”, Diskr. Mat., 20:1 (2008), 145–150; Discrete Math. Appl., 18:1 (2008), 79–84

Citation in format AMSBIB
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\by M.~A.~Cherepnev
\paper A block algorithm of Lanczos type for solving sparse systems of linear equations
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 1
\pages 145--150
\mathnet{http://mi.mathnet.ru/dm997}
\crossref{https://doi.org/10.4213/dm997}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2420505}
\zmath{https://zbmath.org/?q=an:1173.65315}
\elib{http://elibrary.ru/item.asp?id=20730237}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 1
\pages 79--84
\crossref{https://doi.org/10.1515/DMA.2008.006}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-64549154796}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Cherepnev M.A., “O nekotorykh vychisleniyakh v prostranstvakh krylova nad GF(2)”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 14:4 (2009), 833–835
    2. Cherepniov M.A., “Version of block Lanczos-type algorithm for solving sparse linear systems”, Bulletin Mathematique de La Societe Des Sciences Mathematiques de Roumanie, 53:3 (2010), 225–230  mathscinet  zmath  isi
    3. M. A. Cherepniov, “A connection of series approximations and the basis of the Krylov space in block algorithms of Coppersmith and Montgomery”, J. Math. Sci., 193:4 (2013), 622–630  mathnet  crossref
    4. M. A. Cherepniov, N. L. Zamarashkin, “The universal block Lanczos–Padé method for linear systems over large prime fields”, J. Math. Sci., 221:3 (2017), 461–478  mathnet  crossref  mathscinet
  • Дискретная математика
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