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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 6, Pages 983–995 (Mi zvmmf453)  

This article is cited in 2 scientific papers (total in 2 papers)

Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems

Yu. V. Bychenkov

Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: An algorithm for solving a nonsingular symmetric system of linear equations with a saddle point is examined. This algorithm has two constant iteration parameters and is an extension of the algorithm of Hermitian and skew-Hermitian splitting iterations (the HSS algorithm). Analytical formulas are derived for the optimal values of the iteration parameters. The formulation of the optimization problem is a classical one for the saddle-point problems. The results obtained are sharp.

Key words: saddle-point operator, method of Hermitian and skew-Hermitian splitting iterations, HSS algorithm, GPHSS algorithm.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:6, 937–948

Bibliographic databases:

UDC: 519.614
Received: 20.12.2005

Citation: Yu. V. Bychenkov, “Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 983–995; Comput. Math. Math. Phys., 46:6 (2006), 937–948

Citation in format AMSBIB
\Bibitem{Byc06}
\by Yu.~V.~Bychenkov
\paper Optimization of the generalized method of Hermitian and skew-Hermitian splitting iterations for solving symmetric saddle-point problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 6
\pages 983--995
\mathnet{http://mi.mathnet.ru/zvmmf453}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285359}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 6
\pages 937--948
\crossref{https://doi.org/10.1134/S0965542506060030}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746157304}


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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. Yu. V. Bychenkov, “Preconditioning of saddle point problems by the method of Hermitian and skew-Hermitian splitting iterations”, Comput. Math. Math. Phys., 49:3 (2009), 398–408  mathnet  crossref  mathscinet  isi
    2. Huang Zh.-H., Huang T.-Zh., “Spectral properties of the preconditioned AHSS iteration method for generalized saddle point problems”, Computational & Applied Mathematics, 29:2 (2010), 269–295  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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