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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 Adaptive quadrature ： ウィキペディア英語版 Adaptive quadrature In applied mathematics, adaptive quadrature is a process in which the integral of a function $f(x)$ is approximated using static quadrature rules on adaptively refined subintervals of the integration domain. Generally, adaptive algorithms are just as efficient and effective as traditional algorithms for "well behaved" integrands, but are also effective for "badly behaved" integrands for which traditional algorithms fail. ==General scheme== Adaptive quadrature follows the general scheme 1. procedure integrate ( f, a, b, tau ) 2. $Q\; \backslash approx\; \backslash int\_a^bf(x)\backslash ,\backslash mboxx$ 3. $\backslash varepsilon\; \backslash approx\; \backslash left|Q\; -\; \backslash int\_a^bf(x)\backslash ,\backslash mboxx\backslash right|$ 4. if $\backslash varepsilon\; >\; \backslash tau$ then 5. m = (a + b) / 2 6. Q = integrate(f,a,m,tau/2) + integrate(f,m,b,tau/2) 7. endif 8. return Q An approximation $Q$ to the integral of $f(x)$ over the interval $()$ is computed (line 2), as well as an error estimate $\backslash varepsilon$ (line 3). If the estimated error is larger than the required tolerance $\backslash tau$(line 4), the interval is subdivided (line 5) and the quadrature is applied on both halves separately (line 6). Either the initial estimate or the sum of the recursively computed halves is returned (line 7). The important components are the quadrature rule itself :$Q\; \backslash approx\; \backslash int\_a^bf(x)\backslash ,\backslash mboxx\; ,$ the error estimator :$\backslash varepsilon\; \backslash approx\; \backslash left|Q\; -\; \backslash int\_a^bf(x)\backslash ,\backslash mboxx\backslash right|\; ,$ and the logic for deciding which interval to subdivide, and when to terminate. There are several variants of this scheme. The most common will be discussed later. 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「Adaptive 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.