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Direct global Lanczos method for large linear systems with multiple right-hand sides

  • S. Elgharbi
  • M. EsghirEmail author
  • O. Ibrihich
  • B. Abouzaid
  • M. Essaouini
  • S. El Hajji
Article
  • 12 Downloads

Abstract

The present paper presents a new variant of global nonsymmetric Lanczos method for solving nonsymmetric linear large systems with multiple right-hand sides. Numerical experiments are reported to illustrate the behavior and the efficiency of our proposed method.

Keywords

Global iterative methods Global Lanczos process Nonsymmetric linear systems Multiple right-hand sides Schur complement 

Mathematics Subject Classification

65F10 65F25 

Notes

References

  1. 1.
    Bouyouli, R.: Analyse de la convergence des méthodes GMRES et ARNOLDI: cas standard, global, bloc, thesis. University of Mohammed V, Faculty of Sciences, Rabat (2005)Google Scholar
  2. 2.
    Chu, C.C., Lai, M.H., Feng, W.S.: The multiple point global Lanczos method for mutiple-inputs multiple-outputs interconnect order reduction. IECE Trans. Electron. E89–A, 27062716 (2006)Google Scholar
  3. 3.
    Esghir, M.: Birecursive interpolation algorithm: a formalism for solving systems of linear equations. Appl. Math. Sci. 7(24), 1157–1169 (2013)MathSciNetGoogle Scholar
  4. 4.
    Esghir, M., Elalami, N.: New implementation for nonsymmetric Lanczos method. Appl. Math. Sci. 7(49), 2407–2419 (2013)MathSciNetGoogle Scholar
  5. 5.
    Esghir, M., Louartassi, Y., Elalami, N.: New algorithm for computing transfer function from state equation. Appl. Math. Sci. 7(24), 1171–1182 (2013)MathSciNetGoogle Scholar
  6. 6.
    Esghir, M., Ibrihich, O., Essaouini, M., El Hajji, S.: Transfer function matrices of state-space models. Appl. Math. Sci. 9(19), 935–948 (2015)Google Scholar
  7. 7.
    Esghir, M., Ibrihich, O., Elgharbi, S., Essaouini, M., El Hajji, S.: Solving large linear systems with multiple right-hand sides. In: International conference on engineering and technology (ICET). IEEE (2017)Google Scholar
  8. 8.
    Freund, R., Malhotra, M.: A Block-QMR algorithm for non-Hermitian linear systems with multiple right-hand sides. Linear Algebra Appl. 254, 119157 (1997)MathSciNetCrossRefGoogle Scholar
  9. 9.
    http://math.nist.gov/MatrixMarket. Accessed 20 Apr 2018
  10. 10.
    Jbilou, K., Messaoudi, A., Tebaa, K.: Some Schur complement identities and application to matrix extrapolation methods. Linear Algebra Appl. 392, 195–210 (2004)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jbilou, K., Sadok, H., Tinzefte, A.: Oblique projection methods for linear systems with multiple right-hand sides. Electron. Trans. Numer. Anal. 20, 119–138 (2005)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Lin, Y.Q.: Implicitly restarted global FOM and GMRES for nonsymmetric matrix equations and Sylvester equations. App. Math. Comput. 167–2, 1004–1025 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Robbe, M., Sadkane, M.: Exact and inexact breakdowns in the block GMRES method. Linear Algebra Appl. 419, 265285 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Saad, Y.: Iterative Methods for Solving Sparse Linear Systems. PWS Publishing Compagny, Boston (1996)zbMATHGoogle Scholar
  15. 15.
    Tinzefte, A.: Etude algorithmique et théorique de quelques méthodes de type Lanczos thesis. Université des Sciences et technologies de Lille, Lille (2006)Google Scholar
  16. 16.
    Zhang, J., Dai, H., Zhao, J.: Generalized global conjugate gradient squared algorithm. Appl. Math. Comput. 216, 36943706 (2010)MathSciNetGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  • S. Elgharbi
    • 1
  • M. Esghir
    • 1
    Email author
  • O. Ibrihich
    • 2
  • B. Abouzaid
    • 3
  • M. Essaouini
    • 4
  • S. El Hajji
    • 1
  1. 1.Laboratory of Mathematics, Computing and Applications, Faculty of SciencesMohammed V University in RabatRabatMorocco
  2. 2.Département de Génie réseaux et Télécommunications, Ecole Nationale des Sciences Appliquées de KhouribgaHassan I University in SettatSettatMorocco
  3. 3.Ecole Nationale des Sciences Appliquées d’El JadidaChouaib Doukkali University in El JadidaEl JadidaMorocco
  4. 4.Faculty of SciencesChouaib Doukkali University in El JadidaEl JadidaMorocco

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