  We present an algorithm for computing a spectral decomposition of an interval
matrix as an enclosure of spectral decompositions of particular realizations of
interval matrices. The algorithm relies on tight outer estimations of
eigenvalues and eigenvectors of corresponding interval matrices. We present a
method for general interval matrices as well as its modification for symmetric
interval matrices. As an illustration, we apply the spectral decomposition to
computing powers of interval matrices. Numerical results suggest that a simple
binary exponentiation is more efficient for smaller exponents, but our approach
becomes better when computing higher powers or powers of a special type of
matrices. In particular, we consider symmetric interval and circulant interval
matrices. In both cases we utilize some properties of the corresponding classes
of matrices to make the power computation more efficient.
