翻訳と辞書 Words near each other ・ Jacobethan ・ Jacobetty Rosa ・ Jacobi ・ Jacobi (crater) ・ Jacobi (surname) ・ Jacobi coordinates ・ Jacobi eigenvalue algorithm ・ Jacobi elliptic functions ・ Jacobi field ・ Jacobi form ・ Jacobi group ・ Jacobi identity ・ Jacobi integral ・ Jacobi matrix ・ Jacobi Medical Center ・ Jacobi method ・ Jacobi method for complex Hermitian matrices ・ Jacobi operator ・ Jacobi polynomials ・ Jacobi Robinson ・ Jacobi rotation ・ Jacobi set ・ Jacobi sum ・ Jacobi symbol ・ Jacobi theta functions (notational variations) ・ Jacobi triple product ・ Jacobi zeta function ・ Jacobi's formula ・ Jacobi's four-square theorem ・ Jacobi's theorem Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Jacobi method ： ウィキペディア英語版 Jacobi method In numerical linear algebra, the Jacobi method (or Jacobi iterative method) is an algorithm for determining the solutions of a diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. == Description == Let :$A\backslash mathbf\; x\; =\; \backslash mathbf\; b$ be a square system of ''n'' linear equations, where: Then ''A'' can be decomposed into a diagonal component ''D'', and the remainder ''R'': : The solution is then obtained iteratively via :$\backslash mathbf^\; =\; D^\; (\backslash mathbf\; -\; R\; \backslash mathbf^),$ where $\backslash mathbf^$ is the ''k''th approximation or iteration of $\backslash mathbf$ and $\backslash mathbf^$ is the next or ''k'' + 1 iteration of $\backslash mathbf$. The element-based formula is thus: :$x^\_i\; =\; \backslash fraca\_x^\_j\backslash right),\backslash quad\; i=1,2,\backslash ldots,n.$ The computation of ''x''''i''(''k''+1) requires each element in x(''k'') except itself. Unlike the Gauss–Seidel method, we can't overwrite ''x''''i''(''k'') with ''x''''i''(''k''+1), as that value will be needed by the rest of the computation. The minimum amount of storage is two vectors of size ''n''. 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「Jacobi 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.