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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 Rayleigh–Ritz method ： ウィキペディア英語版 Rayleigh–Ritz method The Rayleigh–Ritz method (after Walther Ritz and Lord Rayleigh) is a widely used method used to approximate eigenvalues and eigenvectors. == Description of method == The Rayleigh–Ritz method allows for the computation of Ritz pairs $(\backslash tilde\_i,\backslash tilde\; =\; \backslash lambda\; \backslash textbf$ Where $A\; \backslash in\; \backslash mathbb^$. The procedure is as follows:〔G. Schofield, J. R. Chelikowsky, Y. Saad (2011). pg 6〕 # Compute an orthonormal basis $V\; \backslash in\; \backslash mathbb^$ approximating the eigenspace corresponding to m eigenvectors # Compute $R\; \backslash gets\; V^$ * A V # Compute the eigenvalues of R solving $R\; \backslash mathbf\_i\; =\; \backslash tilde\_i\; \backslash mathbf\_i$ # Form the ritz pairs $(\backslash tilde\_i,\backslash tilde\_i,V\; \backslash textbf\_i)$ One can always compute the accuracy of such an approximation via $\backslash |\; A\; \backslash tilde\_i\; \backslash tilde\{\backslash textbf\{x\}\}\_i\backslash |$ If a Krylov subspace is used and A is a general matrix, then this is the Arnoldi 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「Rayleigh–Ritz 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.