Error Bounds on the Spectral Radius of Uncertain Matrices

We deal with the problem of bounding spectral radius of uncertain matrices. We suppose that uncertainties are estimated by lower and upper limits, and the aim is to find the upper bound of the maximum spectral radius of such interval matrices. The upper limit for the spectral radius is difficult to find but it is important, e.g., for testing the Schur stability of discrete dynamical systems. We propose two cheap and tight formulae to compute the demanding upper bounds; they are based on reductions to the case of symmetric interval matrices. Further, we adapt the filtering method to refine the computed values.