  The problem of construction of Barabanov norms for analysis of properties of
the joint (generalized) spectral radius of matrix sets has been discussed in a
number of publications. The method of Barabanov norms was the key instrument in
disproving the Lagarias-Wang Finiteness Conjecture. The related constructions
were essentially based on the study of the geometrical properties of the unit
balls of some specific Barabanov norms. In this context the situation when one
fails to find among current publications any detailed analysis of the
geometrical properties of the unit balls of Barabanov norms looks a bit
paradoxical. Partially this is explained by the fact that Barabanov norms are
defined nonconstructively, by an implicit procedure. So, even in simplest cases
it is very difficult to visualize the shape of their unit balls. The present
work may be treated as the first step to make up this deficiency. In the paper
two iteration procedure are considered that allow to build numerically
Barabanov norms for the irreducible matrix sets and simultaneously to compute
the joint spectral radius of these sets.
