[Sur la convergence de la méthode de Jacobi–Davidson appliquée à un problème aux valeurs propres généralisé]
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.
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.
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@article{CRMATH_2007__345_5_293_0,
author = {Hechme, Grace},
title = {Convergence analysis of the {Jacobi{\textendash}Davidson} method applied to a generalized eigenproblem},
journal = {Comptes Rendus. Math\'ematique},
pages = {293--296},
publisher = {Elsevier},
volume = {345},
number = {5},
year = {2007},
doi = {10.1016/j.crma.2007.07.003},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.07.003/}
}
TY - JOUR AU - Hechme, Grace TI - Convergence analysis of the Jacobi–Davidson method applied to a generalized eigenproblem JO - Comptes Rendus. Mathématique PY - 2007 SP - 293 EP - 296 VL - 345 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.07.003/ DO - 10.1016/j.crma.2007.07.003 LA - en ID - CRMATH_2007__345_5_293_0 ER -
%0 Journal Article %A Hechme, Grace %T Convergence analysis of the Jacobi–Davidson method applied to a generalized eigenproblem %J Comptes Rendus. Mathématique %D 2007 %P 293-296 %V 345 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.07.003/ %R 10.1016/j.crma.2007.07.003 %G en %F CRMATH_2007__345_5_293_0
Hechme, Grace. Convergence analysis of the Jacobi–Davidson method applied to a generalized eigenproblem. Comptes Rendus. Mathématique, Tome 345 (2007) no. 5, pp. 293-296. doi : 10.1016/j.crma.2007.07.003. http://www.numdam.org/articles/10.1016/j.crma.2007.07.003/
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[2] Computational Methods for Fluid Flow, Springer Series in Computational Physics, Springer-Verlag, New York, 1983
[3] Numerical Methods for Large Eigenvalue Problems, Algorithms and Architectures for Advanced Scientific Computing, Manchester University Press, Manchester, UK, 1992
[4] Jacobi–Davidson type methods for generalized eigenproblems and polynomial eigenproblems, BIT, Volume 36 (1996) no. 3, pp. 595-633
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