  In this paper, we investigate the convergence speed of the Arimoto-Blahut
algorithm. For many channel matrices the convergence is exponential, but for
some channel matrices it is slower than exponential. By analyzing the Taylor
expansion of the defining function of the Arimoto-Blahut algorithm, we will
make the conditions clear for the exponential or slower convergence. The
analysis of the slow convergence is new in this paper. Based on the analysis,
we will compare the convergence speed of the Arimoto-Blahut algorithm
numerically with the values obtained in our theorems for several channel
matrices. The purpose of this paper is a complete understanding of the
convergence speed of the Arimoto-Blahut algorithm.
