An Algorithm for the Real Interval Eigenvalue Problem

Milan Hladik (1, 2) , David Daney (1) , Elias P. P. Tsigaridas (3)

1 COPRIN - Constraints solving, optimization and robust interval analysis
2 KAM - Department of Applied Mathematics [Prague]
3 NKUA - National and Kapodistrian University of Athens

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 so- phisticated 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).

Mots clés: Interval matrix; real eigenvalue; eigenvalue bounds; regularity; interval analysis.; interval analysis

Domaines: Analyse numérique [math.NA]

Milan Hladik, David Daney, Elias P. P. Tsigaridas. An Algorithm for the Real Interval Eigenvalue Problem. [Research Report] RR-6680, INRIA. 2008, pp.28. ⟨inria-00329714⟩