  The problem of computing $\alpha$-capacity for $\alpha>1$ is equivalent to
that of computing the correct decoding exponent. Various algorithms for
computing them have been proposed, such as Arimoto and Jitsumatsu--Oohama
algorithm. In this study, we propose a novel alternating optimization algorithm
for computing the $\alpha$-capacity for $\alpha>1$ based on a variational
characterization of the Augustin--Csisz{\'a}r mutual information. A comparison
of the convergence performance of these algorithms is demonstrated through
numerical examples.
