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The crystal structure of the intermediate phase (3MgO·2CO 2 ) of synthetic nesquehonite (MgO·3H 2 O) following heat treatment was solved by Monte Carlo simulation using powder X-ray diffraction data and was confirmed by Rietveld refinement. The phase is cubic with space group I43m and cell constants of a = 8.516(13)Å. The unit cell consists of independent atoms such as magnesium, carbon, and two oxygen atoms. The magnesium atom is surrounded by six oxygen atoms in octahedral coordination, and four symmetrically identical MgO 6 octahedra in a edge-sharing arrangement form an Mg 4 O 17 block in the (100) planes of a unit cell. These Mg 4 O 17 blocks share edges with other Mg 4 O 17 blocks to form a framework structure. A CO 3 triangle that exists on the three-fold axis connects three Mg 4 O 17 blocks.

In this paper, we investigate the convergence speed of the Arimoto algorithm. By analyzing the Taylor expansion of the defining function of the Arimoto algorithm, we will clarify the conditions for the exponential or 1/N order convergence and calculate the convergence speed. We show that the convergence speed of the 1/N order is evaluated by the derivatives of the Kullback-Leibler divergence with respect to the input probabilities. The analysis for the convergence of the 1/N order is new in this paper. Based on the analysis, we will compare the convergence speed of the Arimoto algorithm with the theoretical values obtained in our theorems for several channel matrices.