An Algorithm for the Real Interval Eigenvalue Problem
نویسندگان
چکیده
In this paper we present an algorithm for approximating the range of the real eigenvalues of interval matrices. Such matrices could be used to model real-life problems, where data sets suffer from bounded variations such as uncertainties (e.g. tolerances on parameters, measurement errors), or to study problems for given states. The algorithm that we propose is a subdivision algorithm that exploits sophisticated techniques from interval analysis. The quality of the computed approximation, as well as the running time of the algorithm depend on a given input accuracy. We also present an efficient C++ implementation and illustrate its efficiency on various data sets. In most of the cases we manage to compute efficiently the exact boundary points (limited by floating point representation). Key-words: Interval matrix, real eigenvalue, eigenvalue bounds, regularity, interval analysis. ∗ 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 03 29 71 4, v er si on 1 13 O ct 2 00 8 Un algorithme pour le calcul de valeurs propres réelles de matrices d’intervalles Résumé : Mots-clés : in ria -0 03 29 71 4, v er si on 1 13 O ct 2 00 8 An Algorithm for the Real Interval Eigenvalue Problem 3
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