no. 11
Analyse numérique/Analyse fonctionnelle
Image numérique, GMRES et polynômes de Faber
[Numerical range, GMRES and Faber polynomials]
Presented by: Philippe G. Ciarlet
Beckermann, Bernhard1
1Laboratoire Paul-Painlevé, UMR 8524 (ANO-EDP), UFR mathématiques – M3, UST Lille, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 855-860

Soit Fn le polynôme de Faber de degré n associé à l'image numérique d'un opérateur linéaire continu A sur un espace de Hilbert. Nous montrons dans un premier temps que ‖Fn(A)‖⩽2. Nous en déduisons ensuite, en terme d'image numérique, de nouvelles estimations d'erreur pour la méthode GMRES, méthode itérative adaptée à la résolution des systèmes linéaires non-hermitiens.

We first show that ‖Fn(A)‖⩽2, where A is a linear continuous operator acting in a Hilbert space, and Fn is the Faber polynomial of degree n corresponding to the numerical range of A. Then we deduce several new error bounds based on the numerical range for GMRES, an iterative method for solving non-Hermitian systems of linear equations.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.04.027

Beckermann, Bernhard  1

1 Laboratoire Paul-Painlevé, UMR 8524 (ANO-EDP), UFR mathématiques – M3, UST Lille, 59655 Villeneuve d'Ascq cedex, France 
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Beckermann, Bernhard. Image numérique, GMRES et polynômes de Faber. Comptes Rendus. Mathématique, Volume 340 (2005) no. 11, pp. 855-860. doi: 10.1016/j.crma.2005.04.027

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