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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 modulus of smoothness ： ウィキペディア英語版 modulus of smoothness In mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are used in approximation theory and numerical analysis to estimate errors of approximation by polynomials and splines. ==Moduli of smoothness== The modulus of smoothness of order $n$ 〔DeVore, Ronald A., Lorentz, George G., Constructive approximation, Springer-Verlag, 1993.〕 of a function $f\backslash in\; C()$ is the function $\backslash omega\_n:\}\backslash sup\_|\backslash Delta\_h^n(f,x)|\backslash text0\backslash le\; t\backslash le\; \backslash frac\; n,$ and :$\backslash omega\_n(t,f,())=\backslash omega\_n\backslash left(\backslash frac,f,()\backslash right),\backslash textt>\backslash frac,$ where we the finite difference (''n''-th order forward difference) are defined as :$\backslash Delta\_h^n(f,x\_0)=\backslash sum\_^n(-1)^\backslash binom\; f(x\_0+ih).$ 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「modulus of smoothness」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.