Numerical analysis
An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems
Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 696-705.

This work deals with an a posteriori error estimator for Hermitian positive eigenvalue problems. The proposed estimator is based on the residual and the definition of suitable shifts in the matrix spectrum. The mathematical properties (certification and sharpness) are investigated and some numerical experiments are proposed.

L'objet de ce travail est la mise au point et l'étude d'un estimateur a posteriori pour les problèmes aux valeurs propres hermitiens positifs. L'estimateur proposé se base sur une approximation de la rélation entre l'erreur et le résidu du problème. Les propriétés mathématiques de l'estimateur sont étudiées. Des experiences numériques sont proposées afin de valider l'estimateur.

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Published online:
DOI: 10.1016/j.crma.2018.04.017
Bakhta, Athmane 1; Lombardi, Damiano 2

1 École des ponts ParisTech, France
2 INRIA, France
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Bakhta, Athmane; Lombardi, Damiano. An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems. Comptes Rendus. Mathématique, Volume 356 (2018) no. 6, pp. 696-705. doi : 10.1016/j.crma.2018.04.017. http://www.numdam.org/articles/10.1016/j.crma.2018.04.017/

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