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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 Laguerre's method ： ウィキペディア英語版 Laguerre's method In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically solve the equation :$\backslash \; p(x)\; =\; 0$ for a given polynomial ''p''. One of the most useful properties of this method is that it is, from extensive empirical study, very close to being a "sure-fire" method, meaning that it is almost guaranteed to always converge to ''some'' root of the polynomial, no matter what initial guess is chosen. This method is named in honour of Edmond Laguerre, a French mathematician. ==Definition== The algorithm of the Laguerre method to find one root of a polynomial ''p'' of degree ''n'' is: * Choose an initial guess $x\_0$ * For ''k'' = 0, 1, 2, … * * If $p(x\_k)$ is very small, exit the loop * * Calculate $G\; =\; \backslash frac$ * * Calculate $H\; =\; G^2\; -\; \backslash frac$ * * Calculate $a\; =\; \backslash frac\; =\; x\_k\; -\; a$ * Repeat until ''a'' is small enough or if the maximum number of iterations has been reached. If a root has been found, the corresponding linear factor can be removed from ''p''. This deflation step reduces the degree of the polynomial by one, so that eventually, approximations for all roots of ''p'' can be found. Note however that deflation can lead to approximate factors that differ significantly from the corresponding exact factors. This error is least if the roots are found in the order of increasing magnitude. 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「Laguerre's method」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.