Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 6, Pages 975–982 (Mi zvmmf452)  

A minimal residual method for linear polynomials in unitary matrices

M. Danaa, 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, called MINRES-N2, that is based on the use of unconventional Krylov subspaces was previously proposed by the authors for solving a system of linear equations $Ax=b$ with a normal coefficient matrix whose spectrum belongs to an algebraic second-degree curve $\Gamma$. However, the computational scheme of this method does not cover matrices of the form $A=\alpha U+\beta I$, where $U$ is an arbitrary unitary matrix; for such matrices, $\Gamma$ is a circle. Systems of this type are repeatedly solved when the eigenvectors of a unitary matrix are calculated by inverse iteration. In this paper, a modification of MINRES-N2 suitable for linear polynomials in unitary matrices is proposed. Numerical results are presented demonstrating the significant superiority of the modified method over GMRES as applied to systems of this class.

Key words: linear polynomials in unitary matrices, minimal residual method, modification of the MINRES-N2 algorithm.

Full text: PDF file (1162 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2006, 46:6, 930–936

Bibliographic databases:

UDC: 519.614
Received: 26.08.2005

Citation: M. Dana, Kh. D. Ikramov, “A minimal residual method for linear polynomials in unitary matrices”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 975–982; Comput. Math. Math. Phys., 46:6 (2006), 930–936

Citation in format AMSBIB
\Bibitem{DanIkr06}
\by M.~Dana, Kh.~D.~Ikramov
\paper A~minimal residual method for linear polynomials in unitary matrices
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 6
\pages 975--982
\mathnet{http://mi.mathnet.ru/zvmmf452}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2285358}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 6
\pages 930--936
\crossref{https://doi.org/10.1134/S0965542506060029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746133903}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf452
  • http://mi.mathnet.ru/eng/zvmmf/v46/i6/p975

    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
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:570
    Full text:339
    References:44
    First page:1

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