Numerical Algorithms

, Volume 71, Issue 2, pp 383–394 | Cite as

Algorithms for the CMRH method for dense linear systems

  • Sébastien Duminil
  • Mohammed Heyouni
  • Philippe Marion
  • Hassane Sadok
Original Paper


The CMRH (Changing Minimal Residual method based on the Hessenberg process) method is a Krylov subspace method for solving large linear systems with non-symmetric coefficient matrices. CMRH generates a (non orthogonal) basis of the Krylov subspace through the Hessenberg process, and minimizes a quasi-residual norm. On dense matrices, the CMRH method is less expensive and requires less storage than other Krylov methods. In this work, we describe Matlab codes for the best of these implementations. Fortran codes for sequential and parallel implementations are also presented.


Linear systems Krylov method Hessenberg process Dense matrix CMRH method 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Sébastien Duminil
    • 1
  • Mohammed Heyouni
    • 2
  • Philippe Marion
    • 1
  • Hassane Sadok
    • 1
  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité du Littoral Côte d’Opale, Centre Universitaire de la Mi-VoixCalais cedexFrance
  2. 2.ENSAH, Ecole Nationale des Sciences Appliquées d’Al-HoceimaUniversité Mohammed PremierOujdaMaroc

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