Characterizing and approximating eigenvalue sets of symmetric interval matrices

Abstrakt

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.

Klíčová slova

• eigenvalues
• symmetric matrix
• interval matrix