Characterizing and approximating eigenvalue sets of symmetric interval matrices

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

1 KAM - Department of Applied Mathematics [Prague]
2 COPRIN - Constraints solving, optimization and robust interval analysis
3 Department of Computer Science [Aarhus]

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner approximation algorithm, that in many case estimates exact bounds. To our knowledge, this is the first algorithm that is able to guaran- tee exactness. We illustrate our approach by several examples and numerical experiments.

Mots clés: Interval matrix; symmetric matrix; interval analysis; eigenvalue; eigenvalue bounds

Domaines: Robotique [cs.RO]

Milan Hladik, David Daney, Elias Tsigaridas. Characterizing and approximating eigenvalue sets of symmetric interval matrices. [Research Report] RR-7544, INRIA. 2011, pp.22. ⟨inria-00567385⟩