Comptes Rendus
no. 5
Numerical Analysis
Convergence analysis of the Jacobi–Davidson method applied to a generalized eigenproblem

Presented by: Olivier Pironneau

Grace Hechme1
1 Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75739 Paris cedex 15, France
Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 293-296.

In this Note we consider the Jacobi–Davidson method applied to a nonsymmetric generalized eigenproblem. We analyze the convergence behavior of the method when the linear systems involved, known as the correction equations, are solved approximately. Our analysis also exhibits quadratic convergence when the corrections are solved exactly.

Dans cette Note, la méthode de Jacobi–Davidson appliquée à un problème aux valeurs propres généralisé non symétrique est considérée. Nous analysons la convergence de la méthode quand les systèmes linéaires mis en jeu, plus connus sous le nom d'équations de correction, sont résolus approximativement. Notre analyse montre également la convergence quadratique de la méthode pour des solutions exactes de la correction.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.07.003

Grace Hechme 1

1 Laboratoire POEMS, UMR 2706 CNRS/ENSTA/INRIA, École nationale supérieure de techniques avancées, 32, boulevard Victor, 75739 Paris cedex 15, France 
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Grace Hechme. Convergence analysis of the Jacobi–Davidson method applied to a generalized eigenproblem. Comptes Rendus. Mathématique, Volume 345 (2007) no. 5, pp. 293-296. doi : 10.1016/j.crma.2007.07.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.003/

[1] G. Hechme, Theoretical and numerical spectral analysis of some linearized hydrodynamic models, Ph.D. thesis, Universit é de Bretagne Occidentale, Brest, December 2005 (in French); http://www.ensta.fr/~hechme/new/these.html

[2] R. Peyret; T.D. Taylor Computational Methods for Fluid Flow, Springer Series in Computational Physics, Springer-Verlag, New York, 1983

[3] Y. Saad Numerical Methods for Large Eigenvalue Problems, Algorithms and Architectures for Advanced Scientific Computing, Manchester University Press, Manchester, UK, 1992

[4] G.L. Sleijpen; A.G. Booten; D.R. Fokkema; H.A. Van Der Vorst Jacobi–Davidson type methods for generalized eigenproblems and polynomial eigenproblems, BIT, Volume 36 (1996) no. 3, pp. 595-633

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