New convergence results on the global GMRES method for diagonalizable matrices

Authors:
M. Bellalij;K. Jbilou;H. Sadok
Affiliations:
Université de Valenciennes, Le Mont Houy, 59313 Valenciennes Cedex, France;Université du Littoral, zone universitaire de la Mi-voix, batiment H. Poincarré, 50 rue F. Buisson, BP 699, F-62280 Calais Cedex, France;Université du Littoral, zone universitaire de la Mi-voix, batiment H. Poincarré, 50 rue F. Buisson, BP 699, F-62280 Calais Cedex, France
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 5
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Abstract

In the present paper, we give some new convergence results of the global GMRES method for multiple linear systems. In the case where the coefficient matrix A is diagonalizable, we derive new upper bounds for the Frobenius norm of the residual. We also consider the case of normal matrices and we propose new expressions for the norm of the residual.