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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 Shanks transformation ： ウィキペディア英語版 Shanks transformation In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence. This method is named after Daniel Shanks, who rediscovered this sequence transformation in 1955. It was first derived and published by R. Schmidt in 1941.〔Weniger (2003).〕 ==Formulation== For a sequence $\backslash left\backslash \_^\backslash infty\; a\_m\backslash ,$ is to be determined. First, the partial sum $A\_n$ is defined as: :$A\_n\; =\; \backslash sum\_^n\; a\_m\backslash ,$ and forms a new sequence $\backslash left\backslash \_\backslash ,\; A\_\backslash ,\; -\backslash ,\; A\_n^2\}\}$ and forms a new sequence. The sequence $S(A\_n)$ often converges more rapidly than the sequence $A\_n.$ Further speed-up may be obtained by repeated use of the Shanks transformation, by computing $S^2(A\_n)=S(S(A\_n)),$ $S^3(A\_n)=S(S(S(A\_n))),$ etc. Note that the non-linear transformation as used in the Shanks transformation is essentially the same as used in Aitken's delta-squared process. Both operate on a sequence, but the sequence the Shanks transformation operates on is usually thought of as being a sequence of partial sums, although any sequence may be viewed as a sequence of partial sums. 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「Shanks transformation」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.