A New Algorithm for Computing $\alpha$-Capacity

The problem of computing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex>-capacity for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha &gt; 1$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> -capacity for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha &gt; 1$</tex> based on a variational characterization of the Augustin-Csiszár mutual information. A comparison of the convergence performance of these algorithms is demonstrated through numerical examples.