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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 Richardson extrapolation ： ウィキペディア英語版 Richardson extrapolation In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence. It is named after Lewis Fry Richardson, who introduced the technique in the early 20th century. In the words of Birkhoff and Rota, "its usefulness for practical computations can hardly be overestimated."〔Page 126 of 〕 Practical applications of Richardson extrapolation include Romberg integration, which applies Richardson extrapolation to the trapezoid rule, and the Bulirsch–Stoer algorithm for solving ordinary differential equations. ==Example of Richardson extrapolation== Suppose that we wish to approximate $A^$ *, and we have a method $A(h)$ that depends on a small parameter $h$, so that $A(h)\; =\; A^\backslash ast\; +\; C\; h^n\; +\; o(h^)\backslash ;$ Define a new method $R(h,k)\; :=\; \backslash frac$ Then $R(h,\; k)\; =\; \backslash frac)\; )\; \}\; =\; A^$ * + o(h^). $R(h,k)$ is called the Richardson extrapolation of ''A''(''h''), and has a higher-order error estimate $o(h^)$ compared to $A(h)$. Very often, it is much easier to obtain a given precision by using ''R(h)'' rather than ''A(h')'' with a much smaller '' h' '', which can cause problems due to limited precision (rounding errors) and/or due to the increasing number of calculations needed (see examples below). 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「Richardson 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.