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In applied mathematics, adaptive quadrature is a process in which the integral of a function 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. 3. 4. if 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 to the integral of over the interval is computed (line 2), as well as an error estimate (line 3). If the estimated error is larger than the required tolerance (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 : the error estimator : 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
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