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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 11, Pages 1928–1937 (Mi zvmmf562)  

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

A minimal residual method for a special class of linear systems with normal coefficients matrices

M. Danaa, A. G. Zykovb, Kh. D. Ikramovb

a Faculty of Mathematics, University of Kurdistan, Sanandage, 66177, Islamic Republic of Iran
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

Abstract: A minimal residual method is constructed for the class of linear systems with normal coefficient matrices whose spectra belong to algebraic curves of a low order $k$. From the well-known GMRES algorithm, the proposed method differs by the choice of the subspaces in which approximate solutions are sought; as a consequence, the latter method is described by a short-term recurrence. The case $k=2$ is discussed at length. Numerical results are presented that confirm the significant superiority of the proposed method over the GMRES as applied to the linear systems specified above.

Key words: minimal residual method, system of linear algebraic equations, GMRES, MINRES.

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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:11, 1854–1863

Bibliographic databases:
UDC: 519.612
Received: 04.02.2005

Citation: M. Dana, A. G. Zykov, Kh. D. Ikramov, “A minimal residual method for a special class of linear systems with normal coefficients matrices”, Zh. Vychisl. Mat. Mat. Fiz., 45:11 (2005), 1928–1937; Comput. Math. Math. Phys., 45:11 (2005), 1854–1863

Citation in format AMSBIB
\Bibitem{DanZykIkr05}
\by M.~Dana, A.~G.~Zykov, Kh.~D.~Ikramov
\paper A minimal residual method for a special class of linear systems with normal coefficients matrices
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 11
\pages 1928--1937
\mathnet{http://mi.mathnet.ru/zvmmf562}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2203218}
\zmath{https://zbmath.org/?q=an:1102.65033}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 11
\pages 1854--1863


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. Dana, Kh. D. Ikramov, “Solving systems of linear equations whose matrices are low-rank perturbations of Hermitian matrices, revisited”, J. Math. Sci. (N. Y.), 141:6 (2007), 1608–1613  mathnet  crossref  mathscinet  zmath
    2. M. Dana, Kh. D. Ikramov, “A minimal residual method for linear polynomials in unitary matrices”, Comput. Math. Math. Phys., 46:6 (2006), 930–936  mathnet  crossref  mathscinet
    3. Kh. D. Ikramov, “Improved bounds for the recursion width in congruent type methods for solving systems of linear equations”, J. Math. Sci. (N. Y.), 165:5 (2010), 515–520  mathnet  crossref
    4. M. Ghasemi Kamalvand, Kh. D. Ikramov, “A method of congruent type for linear systems with conjugate-normal coefficient matrices”, Comput. Math. Math. Phys., 49:2 (2009), 203–216  mathnet  crossref  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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