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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–Hermite quadrature ： ウィキペディア英語版 Gauss–Hermite quadrature In numerical analysis, Gauss–Hermite quadrature is a form of Gaussian quadrature 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 ''n'' is the number of sample points used. The ''x''''i'' are the roots of the physicists' version of the Hermite polynomial ''H''''n''(''x'') (''i'' = 1,2,...,''n''), and the associated weights ''w''''i'' are given by 〔Abramowitz, M & Stegun, I A, ''Handbook of Mathematical Functions'', 10th printing with corrections (1972), Dover, ISBN 978-0-486-61272-0. Equation 25.4.46.〕 :$w\_i\; =\; \backslash frac\; \}\; (x\_i)">)^2\}.$ ==Example with change of variable== Let's take a function ''h'' which variable ''y'' is Normally distributed $\backslash mathcal(\backslash mu,\backslash sigma^2)$. The expectation of ''h'' corresponds to the following integral: $E()\; =\; \backslash int\_^\; \backslash frac\; \backslash right)\; h(y)\; dy$ As this doesn't exactly correspond to the Hermite polynomial, we need a change of variable: $x\; =\; \backslash frac\; \backslash Leftrightarrow\; y\; =\; \backslash sqrt\; \backslash sigma\; x\; +\; \backslash mu$ Coupled with the integration by substitution, we obtain: $E()\; =\; \backslash int\_^\; \backslash frac\; \backslash sigma\; x\; +\; \backslash mu)\; dx$ leading to: $E()\; \backslash approx\; \backslash frac^n\; w\_i\; h(\backslash sqrt\; \backslash sigma\; x\_i\; +\; \backslash mu)$ 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–Hermite 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.