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model of influenza a drift
Iterative building of Barabanov norms and computation of the joint
spectral radius for matrix sets
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. In
[18, 21] 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 an iteration procedure is considered that allows to build
numerically Barabanov norms for the irreducible matrix sets and
simultaneously to compute the joint spectral radius of these
sets.