  In this paper we present an efficient iterative method of order six for the
inclusion of the inverse of a given regular matrix. To provide the upper error
bound of the outer matrix for the inverse matrix, we combine point and interval
iterations. The new method is relied on a suitable matrix identity and a
modification of a hyper-power method. This method is also feasible in the case
of a full-rank $m\times n$ matrix, producing the interval sequence which
converges to the Moore-Penrose inverse. It is shown that computational
efficiency of the proposed method is equal or higher than the methods of
hyper-power's type.
