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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 Residual (numerical analysis) ： ウィキペディア英語版 Residual (numerical analysis) Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find ''x'' such that : $f(x)=b.\backslash ,$ Given an approximation ''x''0 of ''x'', the residual is : $b\; -\; f(x\_0)\backslash ,$ whereas the error is : $x\; -\; x\_0\backslash ,$ If we do not know ''x'' exactly, we cannot compute the error but we can compute the residual. ==Residual of the approximation of a function== Similar terminology is used dealing with differential, integral and functional equations. For the approximation $~f\_~$ of the solution $~f~$ of the equation :$T(f)(x)=g(x)$ , the residual can either be the function : $~g(x)~\; -\; ~T(f\_)(x)$ or can be said to be the maximum of the norm of this difference : $\backslash max\_\; |g(x)-T(f\_)(x)|$ over the domain $\backslash mathcal\; X$, where the function $~f\_~$ is expected to approximate the solution $~f~$, or some integral of a function of the difference, for example: : $~\backslash int\_\; |g(x)-T(f\_)(x)|^2~\; x.$ In many cases, the smallness of the residual means that the approximation is close to the solution, i.e., : $~\backslash left|\backslash frac\backslash right|\; \backslash ll\; 1.~$ In these cases, the initial equation is considered as well-posed; and the residual can be considered as a measure of deviation of the approximation from the exact solution. 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「Residual (numerical analysis)」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.