Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

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ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



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Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
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doi:10.1553/etna_vol58s470



doi:10.1553/etna_vol58s470



Thema: natural
Ronny Ramlau, Lothar Reichel (Hg.)


ETNA - Electronic Transactions on Numerical Analysis






ISBN 978-3-7001-8258-0
Online Edition

  Research Article
Open access


F. Bouyghf, A. Messaoudi, H. Sadok
PDF Icon  An enhancement of the convergence of the IDR method ()
S.  470 - 485
doi:10.1553/etna_vol58s470

Open access

Verlag der Österreichischen Akademie der Wissenschaften


doi:10.1553/etna_vol58s470
Abstract:
In this paper, we consider a family of algorithms, called IDR, based on the induced dimension reduction theorem. IDR is a family of efficient short recurrence methods introduced by Sonneveld and Van Gijzen for solving large systems of nonsymmetric linear equations. These methods generate residual vectors that live in a sequence of nested subspaces. We present the IDR(s) method and give two improvements of its convergence. We also define and give a global version of the IDR(s) method and describe a partial and a complete improvement of its convergence. Moreover, we recall the block version and state its improvements. Numerical experiments are provided to illustrate the performances of the derived algorithms compared to the well-known classical GMRES method and the bi-conjugate gradient stabilized method for systems with a single right-hand side, as well as the global GMRES, the global bi-conjugate gradient stabilized, the block GMRES, and the block bi-conjugate gradient stabilized methods for systems with multiple right-hand sides.

Keywords:  linear equations, iterative methods, IDR method, Krylov subspace, global and block Krylov subspace methods
  2023/07/03 12:29:56
Object Identifier:  0xc1aa5572 0x003e59b4
.

Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.



Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at