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An algorithm for addressing the real interval eigenvalue problem

Milan Hladïk 1, 2 David Daney 1 Elias Tsigaridas 1
1 COPRIN - Constraints solving, optimization and robust interval analysis
CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech
Abstract : 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 and 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).
Keywords : Interval analysis
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Submitted on : Thursday, November 21, 2013 - 4:04:16 PM
Last modification on : Saturday, January 27, 2018 - 1:30:41 AM

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Milan Hladïk, David Daney, Elias Tsigaridas. An algorithm for addressing the real interval eigenvalue problem. Journal of Computational and Applied Mathematics, Elsevier, 2011, 235 (8), pp.2715 - 2730. ⟨10.1016/j.cam.2010.11.022⟩. ⟨hal-00907710⟩

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