  The paper first recalls the Blahut Arimoto algorithm for computing the
capacity of arbitrary discrete memoryless channels, as an example of an
iterative algorithm working with probability density estimates. Then, a
geometrical interpretation of this algorithm based on projections onto linear
and exponential families of probabilities is provided. Finally, this
understanding allows also to propose to write the Blahut-Arimoto algorithm, as
a true proximal point algorithm. it is shown that the corresponding version has
an improved convergence rate, compared to the initial algorithm, as well as in
comparison with other improved versions.
