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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 Uzawa iteration ： ウィキペディア英語版 Uzawa iteration In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems. It is named after Hirofumi Uzawa and was originally introduced in the context of concave programming. == Basic idea == We consider a saddle point problem of the form : * & \end \begin x_1\\ x_2 \end = \begin b_1\\ b_2 \end, where $A$ is a symmetric positive-definite matrix. Multiplying the first row by $B^$ * A^ and subtracting from the second row yields the upper-triangular system : = \begin b_1\\ b_2 - B^ * A^ b_1 \end, where $S\; :=\; B^$ * A^ B denotes the Schur complement. Since $S$ is symmetric positive-definite, we can apply standard iterative methods like the gradient descent method or the conjugate gradient method to : $S\; x\_2\; =\; B^$ * A^ b_1 - b_2 in order to compute $x\_2$. The vector $x\_1$ can be reconstructed by solving : $A\; x\_1\; =\; b\_1\; -\; B\; x\_2.\; \backslash ,$ It is possible to update $x\_1$ alongside $x\_2$ during the iteration for the Schur complement system and thus obtain an efficient algorithm. 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「Uzawa iteration」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.