Numerical Algorithms

, Volume 20, Issue 4, pp 303–321 | Cite as

CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm

  • H. Sadok


The Generalized Minimal Residual (GMRES) method and the Quasi-Minimal Residual (QMR) method are two Krylov methods for solving linear systems. The main difference between these methods is the generation of the basis vectors for the Krylov subspace. The GMRES method uses the Arnoldi process while QMR uses the Lanczos algorithm for constructing a basis of the Krylov subspace.

In this paper we give a new method similar to QMR but based on the Hessenberg process instead of the Lanczos process. We call the new method the CMRH method. The CMRH method is less expensive and requires slightly less storage than GMRES. Numerical experiments suggest that it has behaviour similar to GMRES.

linear systems iterative methods Hessenberg’s method GMRES QMR 65F10 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • H. Sadok
    • 1
  1. 1.Université du Littoral, zone universitaire de la Mi-voix, Bâtiment H. PoincaréCalais CedexFrance

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