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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 Biconjugate gradient method ： ウィキペディア英語版 Biconjugate gradient method In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations :$A\; x=\; b.\backslash ,$ Unlike the conjugate gradient method, this algorithm does not require the matrix $A$ to be self-adjoint, but instead one needs to perform multiplications by the conjugate transpose . ==The algorithm== # Choose initial guess $x\_0\backslash ,$, two other vectors $x\_0^$ * and $b^$ *\, and a preconditioner $M\backslash ,$ # $r\_0\; \backslash leftarrow\; b-A\backslash ,\; x\_0\backslash ,$ # $r\_0^$ * \leftarrow b^ *-x_0^ *\, A^T # $p\_0\; \backslash leftarrow\; M^\; r\_0\backslash ,$ # $p\_0^$ * \leftarrow r_0^ *M^\, # for $k=0,\; 1,\; \backslash ldots$ do ## $\backslash alpha\_k\; \backslash leftarrow\; \backslash ,$ ## $x\_\; \backslash leftarrow\; x\_k\; +\; \backslash alpha\_k\; \backslash cdot\; p\_k\backslash ,$ ## $x\_^$ * \leftarrow x_k^ * + \overline\cdot p_k^ *\, ## $r\_\; \backslash leftarrow\; r\_k\; -\; \backslash alpha\_k\; \backslash cdot\; A\; p\_k\backslash ,$ ## $r\_^$ * \leftarrow r_k^ *- \overline \cdot p_k^ *\, A ## $\backslash beta\_k\; \backslash leftarrow\; r\_\; \backslash over\; r\_k^$ * M^ r_k}\, ## $p\_\; \backslash leftarrow\; M^\; r\_\; +\; \backslash beta\_k\; \backslash cdot\; p\_k\backslash ,$ ## $p\_^$ * \leftarrow r_^ *M^ + \overline\cdot p_k^ *\, In the above formulation, the computed $r\_k\backslash ,$ and $r\_k^$ * satisfy :$r\_k\; =\; b\; -\; A\; x\_k,\backslash ,$ :$r\_k^$ * = b^ * - x_k^ *\, A and thus are the respective residuals corresponding to $x\_k\backslash ,$ and $x\_k^$ *, as approximate solutions to the systems :$A\; x\; =\; b,\backslash ,$ :$x^$ *\, A = b^ *\,; $x^$ * is the adjoint, and $\backslash overline$ is the complex conjugate. 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「Biconjugate gradient 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.