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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 Gauss–Laguerre quadrature ： ウィキペディア英語版 Gauss–Laguerre quadrature In numerical analysis Gauss–Laguerre quadrature is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: :$\backslash int\_^\; e^\; f(x)\backslash ,dx.$ In this case :$\backslash int\_^\; e^\; f(x)\backslash ,dx\; \backslash approx\; \backslash sum\_^n\; w\_i\; f(x\_i)$ where ''x''''i'' is the ''i''-th root of Laguerre polynomial ''L''''n''(''x'') and the weight ''w''''i'' is given by 〔Equation 25.4.45 in 10th reprint with corrections.〕 :$w\_i\; =\; \backslash frac\; (x\_i)">)^2\}.$ ==For more general functions== To integrate the function $f$ we apply the following transformation :$\backslash int\_^f\backslash left(x\backslash right)dx=\backslash int\_^f\backslash left(x\backslash right)e^e^dx=\backslash int\_^g\backslash left(x\backslash right)e^dx$ where $g\backslash left(x\backslash right)\; :=\; e^\; f\backslash left(x\backslash right)$. For the last integral one then uses Gauss-Laguerre quadrature. Note, that while this approach works from an analytical perspective, it is not always numerically stable. 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「Gauss–Laguerre quadrature」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.