  A central object in the interpretation of quantum mechanics of closed systems
with decoherent histories is the decoherence matrix. But only for a very small
number of models one is able to give explicit expressions for its elements. So
numerical methods are required. Unfortunately the dimensions of this matrices
are usually very high, which makes also a direct numerical calculation
impossible. A solution of this problem would be given by a method which only
calculates the dominant matrix elements. This includes to make a decision about
the dominance of an element before it will be calculated. In this paper I will
develop an algorithm that combines the numerical calculation of the elements of
the decoherence matrix with a permanent estimation, so that finally the
dominant elements will be calculated only. As an example I apply this procedure
to the Caldeira- Leggett-modell.
