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An algorithm for addressing the real interval eigenvalue problem

✍ Scribed by Milan Hladík; David Daney; Elias P. Tsigaridas

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
511 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

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).

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