A filtering method for the interval eigenvalue problem

We consider the general problem of computing intervals that contain the real eigenvalues of interval matrices. Given an outer estimation of the real eigenvalue set of an interval matrix, we propose a filtering method that improves the estimation. Even though our method is based on an sufficient regularity condition, it is very efficient in practice, and our experimental results suggest that, in general, improves significantly the input estimation. The proposed method works for general, as well as for symmetric matrices. Key-words: Interval matrix, symmetric matrix, interval analysis, eigenvalue, eigenvalue bounds. ∗ Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranské nám. 25, 118 00, Prague, Czech Republic, e-mail: [email protected] † INRIA Sophia-Antipolis Méditerranée, 2004 route des Lucioles, BP 93, 06902 SophiaAntipolis Cedex, France, e-mail: [email protected] in ria -0 04 22 96 6, v er si on 1 8 O ct 2 00 9 Mthode de filtrage des valeurs propres des matrices intervalles Résumé : Mots-clés : Matrices intervalles, matrices symtriques, valeurs propres, bornes sur les valeurs propres, analyse par intervalles. in ria -0 04 22 96 6, v er si on 1 8 O ct 2 00 9 A filtering method for the interval eigenvalue problem 3