Image numérique, GMRES et polynômes de Faber

Resume Soit F n le polynome de Faber de degre n associe a l'image numerique d'un operateur lineaire continu A sur un espace de Hilbert. Nous montrons dans un premier temps que ‖ F n ( A ) ‖ ⩽ 2 . Nous en deduisons ensuite, en terme d'image numerique, de nouvelles estimations d'erreur pour la methode GMRES, methode iterative adaptee a la resolution des systemes lineaires non-hermitiens. Pour citer cet article : B. Beckermann, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

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