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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Matrix geometric method ： ウィキペディア英語版 Matrix geometric method In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block structure. The method was developed "largely by Marcel F. Neuts and his students starting around 1975." ==Method description== The method requires a transition rate matrix with tridiagonal block structure as follows ::$Q=\backslash begin$ B_ & B_ \\ B_ & A_1 & A_2 \\ & A_0 & A_1 & A_2 \\ && A_0 & A_1 & A_2 \\ &&& A_0 & A_1 & A_2 \\ &&&& \ddots & \ddots & \ddots \end where each of ''B''00, ''B''01, ''B''10, ''A''0, ''A''1 and ''A''2 are matrices. To compute the stationary distribution ''π'' writing ''π'' ''Q'' = 0 the balance equations are considered for sub-vectors ''π''''i'' ::$\backslash begin$ \pi_0 B_ + \pi_1 B_ &= 0\\ \pi_0 B_ + \pi_1 A_1 + \pi_2 A_0 &= 0\\ \pi_1 A_2 + \pi_2 A_1 + \pi_3 A_0 &= 0 \\ & \vdots \\ \pi_ A_2 + \pi_i A_1 + \pi_ A_0 &= 0\\ & \vdots \\ \end Observe that the relationship ::$\backslash pi\_i\; =\; \backslash pi\_1\; R^$ holds where ''R'' is the Neut's rate matrix, which can be computed numerically. Using this we write ::$\backslash begin$ \begin\pi_0 & \pi_1 \end \beginB_ & B_ \\ B_ & A_1 + RA_0 \end = \begin 0 & 0 \end \end which can be solve to find ''π''0 and ''π''1 and therefore iteratively all the ''π''''i''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Matrix geometric method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.