[Estimateur a posteriori pour les problèmes aux valeurs propres hermitiens positifs, reposant sur des décalages]
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.
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.
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@article{CRMATH_2018__356_6_696_0,
author = {Bakhta, Athmane and Lombardi, Damiano},
title = {An a posteriori error estimator based on shifts for positive {Hermitian} eigenvalue problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {696--705},
publisher = {Elsevier},
volume = {356},
number = {6},
year = {2018},
doi = {10.1016/j.crma.2018.04.017},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2018.04.017/}
}
TY - JOUR AU - Bakhta, Athmane AU - Lombardi, Damiano TI - An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems JO - Comptes Rendus. Mathématique PY - 2018 SP - 696 EP - 705 VL - 356 IS - 6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2018.04.017/ DO - 10.1016/j.crma.2018.04.017 LA - en ID - CRMATH_2018__356_6_696_0 ER -
%0 Journal Article %A Bakhta, Athmane %A Lombardi, Damiano %T An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems %J Comptes Rendus. Mathématique %D 2018 %P 696-705 %V 356 %N 6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2018.04.017/ %R 10.1016/j.crma.2018.04.017 %G en %F CRMATH_2018__356_6_696_0
Bakhta, Athmane; Lombardi, Damiano. An a posteriori error estimator based on shifts for positive Hermitian eigenvalue problems. Comptes Rendus. Mathématique, Tome 356 (2018) no. 6, pp. 696-705. doi : 10.1016/j.crma.2018.04.017. http://archive.numdam.org/articles/10.1016/j.crma.2018.04.017/
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