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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 Newton's method in optimization ： ウィキペディア英語版 Newton's method in optimization In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation ). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to ), also known as the stationary points of . ==Method== In the one-dimensional problem, Newton's method attempts to construct a sequence from an initial guess that converges towards some value satisfying . This is a stationary point of . The second order Taylor expansion of around is: :$f\_T(x)=f\_T(x\_n+\backslash Delta\; x)\; \backslash approx\; f(x\_n)+f\text{'}(x\_n)\backslash Delta\; x+\backslash frac\; 1\; 2\; f\text{'}\text{'}(x\_n)\; \backslash Delta\; x^2$. We want to find such that is maximum. We seek to solve the equation that sets the derivative of this least expression with respect to equal to zero: :$\backslash displaystyle\; 0\; =\; \backslash frac\; \backslash left(f(x\_n)+f\text{'}(x\_n)\backslash Delta\; x+\backslash frac\; 1\; 2\; f\text{'}\text{'}(x\_n)\; \backslash Delta\; x^2\backslash right)\; =\; f\text{'}(x\_n)+f\text{'}\text{'}\; (x\_n)\; \backslash Delta\; x$. For the value of , which is the solution of this equation, it can be hoped that will be closer to a stationary point . Provided that is a twice-differentiable function and other technical conditions are satisfied, the sequence will converge to a point satisfying . 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「Newton's method in optimization」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.