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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 Golden section search ： ウィキペディア英語版 Golden section search The golden section search is a technique for finding the extremum (minimum or maximum) of a strictly unimodal function by successively narrowing the range of values inside which the extremum is known to exist. The technique derives its name from the fact that the algorithm maintains the function values for triples of points whose distances form a golden ratio. The algorithm is the limit of Fibonacci search (also described below) for a large number of function evaluations. Fibonacci search and Golden section search were discovered by Kiefer (1953). (see also Avriel and Wilde (1966)). ==Basic idea== The diagram above illustrates a single step in the technique for finding a minimum. The functional values of $f(x)$ are on the vertical axis, and the horizontal axis is the ''x'' parameter. The value of $f(x)$ has already been evaluated at the three points: $x\_1$, $x\_2$, and $x\_3$. Since $f\_2$ is smaller than either $f\_1$ or $f\_3$, it is clear that a minimum lies inside the interval from $x\_1$ to $x\_3$ (since ''f'' is unimodal). The next step in the minimization process is to "probe" the function by evaluating it at a new value of ''x'', namely $x\_4$. It is most efficient to choose $x\_4$ somewhere inside the largest interval, i.e. between $x\_2$ and $x\_3$. From the diagram, it is clear that if the function yields $f\_$ then a minimum lies between $x\_1$ and $x\_4$ and the new triplet of points will be $x\_1$, $x\_2$, and $x\_4$. However if the function yields the value $f\_$ then a minimum lies between $x\_2$ and $x\_3$, and the new triplet of points will be $x\_2$, $x\_4$, and $x\_3$. Thus, in either case, we can construct a new narrower search interval that is guaranteed to contain the function's minimum. 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「Golden section search」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.