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Algorithms for the CMRH method for dense linear systems

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral Côte d’Opale, Centre Universitaire de la Mi-Voix, Batiment H. Poincaré, 50 Rue F. Buisson, BP 699, 62228, Calais cedex, France

    Sébastien Duminil, Philippe Marion & Hassane Sadok

  2. ENSAH, Ecole Nationale des Sciences Appliquées d’Al-Hoceima, Université Mohammed Premier, Oujda, Maroc

    Mohammed Heyouni

Authors
  1. Sébastien Duminil
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  2. Mohammed Heyouni
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  3. Philippe Marion
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  4. Hassane Sadok
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Correspondence to Hassane Sadok.

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Duminil, S., Heyouni, M., Marion, P. et al. Algorithms for the CMRH method for dense linear systems. Numer Algor 71, 383–394 (2016). https://doi.org/10.1007/s11075-015-9997-2

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  • DOI: https://doi.org/10.1007/s11075-015-9997-2

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