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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 Minimum polynomial extrapolation ： ウィキペディア英語版 Minimum polynomial extrapolation In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration of vector sequences, due to Sabay and Jackson. While Aitken's method is the most famous, it often fails for vector sequences. An effective method for vector sequences is the minimum polynomial extrapolation. It is usually phrased in terms of the fixed point iteration: : $x\_=f(x\_k).$ Given iterates $x\_1,\; x\_2,\; ...,\; x\_k$ in $\backslash Bbb\; R^n$, one constructs the $n\; \backslash times\; (k-1)$ matrix $U=(x\_2-x\_1,\; x\_3-x\_2,\; ...,\; x\_k-x\_)$ whose columns are the $k-1$ differences. Then, one computes the vector $c=-U^+\; (x\_-x\_k)$ where $U^+$ denotes the Moore–Penrose pseudoinverse of $U$. The number 1 is then appended to the end of $c$, and the extrapolated limit is :$s=,$ where $X=(x\_2,\; x\_3,\; ...,\; x\_)$ is the matrix whose columns are the $k$ iterates starting at 2. The following 4 line MATLAB code segment implements the MPE algorithm: U=x(:,2:end-1)-x(:,1:end-2); c=-pinv(U) *(x(:,end)-x(:,end-1)); c(end+1,1)=1; s=(x(:,2:end) *c)/sum(c); ==References== 〔 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「Minimum polynomial extrapolation」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.