An Algorithm for the Real Interval Eigenvalue Problem

6680 | October 2008 | 25 pagesAbstract: In this paper we present an algorithm for approximating the r angeof the real eigenvalues of interval matrices. Such matrices could be used tomodel real-life problems, where data sets su er from bounde d variations suchas uncertainties (e.g. tolerances on parameters, measurem ent errors), or tostudy problems for given states.The algorithm that we propose is a subdivision algorithm tha t exploits so-phisticated techniques from interval analysis. The qualit y of the computedapproximation, as well as the running time of the algorithm d epend on a giveninput accuracy. We also present an ecient C++ implementati on and illustrateits eciency on various data sets. In most of the cases we mana ge to computeeciently the exact boundary points (limited by oating poi nt representation).Key-words: Interval matrix, real eigenvalue, eigenvalue bounds, regu larity,interval analysis.

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