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Keldysh Institute preprints, 2013, 013, 17 pp. (Mi ipmp13)  

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

Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix

I. E. Kaporin, O. Yu. Milyukova


Abstract: In the paper we consider the iterative solution of linear system $Ax=b$ by the conjugate gradient method using the factorized preconditioner $B=(I+LZ)Y(I+ZU)$, where $A=D+L+U$ is the additive splitting of the coefficient matrix into the strictly lower triangular, the diagonal, and the strictly upper triangular parts. For an arbitrary symmetric positive definite matrix $A$, the diagonal matrices $Y > 0$ and $Z$ are constructed as the minimizers of a certain upper bound for the K-condition number of the inverse preconditioned matrix. The main advantages of the new method are as follows: wide range of applicability, low operation number count per iteration, good parallelizability for all the stages of computation, and sufficient reduction of the iteration number (for a properly chosen preconditioning parameters). Numerical results are given for several test problems.

Keywords: onjugate gradient method, factorized preconditioner, the K-condition number

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Citation: I. E. Kaporin, O. Yu. Milyukova, “Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix”, Keldysh Institute preprints, 2013, 013, 17 pp.

Citation in format AMSBIB
\Bibitem{KapMil13}
\by I.~E.~Kaporin, O.~Yu.~Milyukova
\paper Optimization of the factorized preconditioners of conjugate gradient method for solving the linear algebraic systems with symmetric positive definite matrix
\jour Keldysh Institute preprints
\yr 2013
\papernumber 013
\totalpages 17
\mathnet{http://mi.mathnet.ru/ipmp13}


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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. O. Yu. Milyukova, “Parallelnye varianty metoda nepolnogo treugolnogo razlozheniya vtorogo poryadka sopryazhennykh gradientov na osnove ispolzovaniya spetsialnogo pereuporyadocheniya matritsy koeffitsientov”, Preprinty IPM im. M. V. Keldysha, 2014, 052, 32 pp.  mathnet
    2. O. Yu. Milyukova, “Sochetanie chislovykh i strukturnykh podkhodov k postroeniyu nepolnogo treugolnogo razlozheniya vtorogo poryadka v parallelnykh algoritmakh predobuslovlennogo metoda sopryazhennykh gradientov”, Preprinty IPM im. M. V. Keldysha, 2015, 010, 32 pp.  mathnet
    3. A. Gorobets, “On technology of large-scale CFD simulations”, Math. Models Comput. Simul., 8:6 (2016), 660–670  mathnet  crossref  elib
  • Препринты Института прикладной математики им. М. В. Келдыша РАН
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