  The numerical computation of the exponentiation of a real matrix has been
intensively studied. The main objective of a good numerical method is to deal
with round-off errors and computational cost. The situation is more complicated
when dealing with interval matrices exponentiation: Indeed, the main problem
will now be the dependency loss of the different occurrences of the variables
due to interval evaluation, which may lead to so wide enclosures that they are
useless. In this paper, the problem of computing a sharp enclosure of the
interval matrix exponential is proved to be NP-hard. Then the scaling and
squaring method is adapted to interval matrices and shown to drastically reduce
the dependency loss w.r.t. the interval evaluation of the Taylor series.
