Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
General information
Latest issue
Impact factor

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Zh. Vychisl. Mat. Mat. Fiz.:

Personal entry:
Save password
Forgotten password?

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.

Full text: PDF file (1438 kB)
References: PDF file   HTML file

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
\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
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 11
\pages 1854--1863

Linking options:
  • http://mi.mathnet.ru/eng/zvmmf562
  • http://mi.mathnet.ru/eng/zvmmf/v45/i11/p1928

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru

    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. 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
    Number of views:
    This page:1137
    Full text:809
    First page:1

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021