In [8] (Nakagawa, et.al., IEEE Trans. IT, 2021), we investigated the convergence speed of the Arimoto-Blahut algorithm. In [8], the convergence of the order $O(1/N)$ was analyzed by focusing on the second-order nonlinear recurrence formula consisting of the first- and second-order terms of the Taylor expansion of the defining function of the Arimoto-Blahut algorithm. However, in [8], an infinite number of inequalities were assumed as a "conjecture," and proofs were given based on the conjecture. In this paper, we report a proof of the convergence of the order $O(1/N)$ for a class of channel matrices without assuming the conjecture. The correctness of the proof will be confirmed by several numerical examples.
翻译：在[8] (Nakagawa, et.al., IEEE Trans. IIT, 2021)中,我们调查了Arimoto-Blahut算法的趋同速度。在[8] 中,我们通过侧重于由泰勒扩大Arimoto-Blahut算法定义功能的第一和第二级条件组成的第二级非线性重复计算公式,分析了Arimoto-Blahut算法的趋同速度。然而,在[8] 中,有无限数量的不平等被假定为“预测”,根据推测提供了证据。在本文中,我们报告的证据是,在不假定推测的情况下,对某一类频道矩阵的一等价O(1/N)的汇合。证据的正确性将由几个数字例子证实。
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