  In this work, we investigate the interval generalized Sylvester matrix
equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some
techniques for obtaining outer estimations for the so-called united solution
set of this interval system. First, we propose a modified variant of the
Krawczyk operator which causes reducing computational complexity to cubic,
compared to Kronecker product form. We then propose an iterative technique for
enclosing the solution set. These approaches are based on spectral
decompositions of the midpoints of ${\bf{A}}$, ${\bf{B}}$, ${\bf{C}}$ and
${\bf{D}}$ and in both of them we suppose that the midpoints of ${\bf{A}}$ and
${\bf{C}}$ are simultaneously diagonalizable as well as for the midpoints of
the matrices ${\bf{B}}$ and ${\bf{D}}$. Some numerical experiments are given to
illustrate the performance of the proposed methods.
