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Some results about GMRES in the singular case

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Abstract

In this paper, we study the Generalized Minimal Residual (GMRES) method for solving singular linear systems, particularly when the necessary and sufficient condition to obtain a Krylov solution is not satisfied. Thanks to some new results which may be applied in exact arithmetic or in finite precision, we analyze the convergence of GMRES and restarted GMRES. These formulas can also be used in the case when the systems are nonsingular. In particular, it allows us to understand what is often referred to as stagnation of the residual norm of GMRES.

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  1. Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville, Université du Littoral, zone universitaire de la Mi‐voix, bâtiment H. Poincarré, 50 rue F. Buisson, BP 699, F‐62228, Calais Cedex, France

    L. Smoch

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  1. L. Smoch
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Smoch, L. Some results about GMRES in the singular case. Numerical Algorithms 22, 193–212 (1999). https://doi.org/10.1023/A:1019162908926

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  • DOI: https://doi.org/10.1023/A:1019162908926

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