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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 Lehmer–Schur algorithm ： ウィキペディア英語版 Lehmer–Schur algorithm In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm extending the idea of enclosing roots like in the one-dimensional bisection method to the complex plane. It uses the Schur–Cohn test to test increasingly smaller disks for the presence or absence of roots. Alternative methods like Wilf's algorithm apply different tests to differently shaped areas but keep the idea of descent by subdivision. ==The Lehmer method== The Schur–Cohn test described below allows to determine if a polynomial has no roots in the unit disk and in some cases to determine the exact number of roots. The method proposed by Lehmer test for the presence of roots of a polynomial $p(z)$ on a collection of disks $D(c,\backslash rho)$ in the complex plane by applying the Schur–Cohn test to the shifted and scaled polynomial $p(c+\backslash rho\; z).$ Starting with ''c''=0 and ρ=1, the radius in increased or decreased by factors of 2 until the annulus $\backslash rho\backslash le|z|\backslash le2\backslash rho$ is found to contain roots. Then the method is recursively applied to the 8 disks with center $c\_k=\backslash frac53\backslash rho\; e^$, $k=0,1,\backslash dots,7$ and initial radius $\backslash rho$ (originally $\backslash frac56\backslash rho$, which is slightly too small to cover the full annulus). If after some recursions a small disk is found that contains only one root, this root is further approximated using Newton's method and then the polynomial is deflated by splitting off the corresponding linear factor. After that, the whole procedure is restarted. 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「Lehmer–Schur algorithm」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.