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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 Horner's method ： ウィキペディア英語版 Horner's method In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S.) is either of two things: (i) an algorithm for calculating polynomials, which consists of transforming the monomial form into a computationally efficient form;〔 or (ii) a method for approximating the roots of a polynomial. The latter is also known as Ruffini–Horner's method.〔:fr:Méthode de Ruffini-Horner〕 These methods are named after the British mathematician William George Horner, although they were known before him by Paolo Ruffini〔Florian Cajori, (Horner's method of approximation anticipated by Ruffini ), Bulletin of the American Mathematical Society, Vol. 17, No. 9, pp. 409–414, 1911 (read before the Southwestern Section of the American Mathematical Society on November 26, 1910).〕 and, six hundred years earlier, by the Chinese mathematician Qin Jiushao.〔''It is obvious that this procedure is a Chinese invention'', Ulrich Librecht, Chinese Mathematics in the Thirteenth Century, Chapter 13, '' Equations of Higher Degree'', p178 Dover, ISBN 0-486-44619-0〕 ==Description of the algorithm== Given the polynomial :$p(x)\; =\; \backslash sum\_^n\; a\_i\; x^i\; =\; a\_0\; +\; a\_1\; x\; +\; a\_2\; x^2\; +\; a\_3\; x^3\; +\; \backslash cdots\; +\; a\_n\; x^n,$ where $a\_0,\; \backslash ldots,\; a\_n$ are real numbers, we wish to evaluate the polynomial at a specific value of $x$, say $x\_0$. To accomplish this, we define a new sequence of constants as follows: :$\backslash begin$ b_n & := a_n \\ b_ & := a_ + b_n x_0 \\ & + a_n x))). \, Thus, by iteratively substituting the $b\_i$ into the expression, : $$ \begin p(x_0) & = a_0 + x_0(a_1 + x_0(a_2 + \cdots + x_0(a_ + b_n x_0))) \\ & = a_0 + x_0(a_1 + x_0(a_2 + \cdots + x_0(b_))) \\ & {} \ \ \vdots \\ & = a_0 + x_0(b_1) \\ & = b_0. \end{align} 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「Horner'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.