Characterizing and Approximating Eigenvalue Sets of Symmetric Interval Matrices

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

1 UK - Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic]
2 COPRIN - Constraints solving, optimization and robust interval analysis
3 CS - Department of Computer Science [Aarhus]

We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries are perturbed, with perturbations belonging to 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 guarantee exactness. We illustrate our approach by several examples and numerical experiments.

Mots clés: Eigenvalue; Eigenvalue bounds; Interval analysis; Interval matrix; Symmetric matrix

Domaines: Robotique [cs.RO]

Milan Hladïk, David Daney, Elias P. Tsigaridas. Characterizing and Approximating Eigenvalue Sets of Symmetric Interval Matrices. Computers & Mathematics with Applications, 2011, 62 (8), pp.3152--3163. ⟨10.1016/j.camwa.2011.08.028⟩. ⟨hal-00907534⟩