翻訳と辞書 Words near each other ・ "O" Is for Outlaw ・ "O"-Jung.Ban.Hap. ・ "Ode-to-Napoleon" hexachord ・ "Oh Yeah!" Live ・ "Our Contemporary" regional art exhibition (Leningrad, 1975) ・ "P" Is for Peril ・ "Pimpernel" Smith ・ "Polish death camp" controversy ・ "Pro knigi" ("About books") ・ "Prosopa" Greek Television Awards ・ "Pussy Cats" Starring the Walkmen ・ "Q" Is for Quarry ・ "R" Is for Ricochet ・ "R" The King (2016 film) ・ "Rags" Ragland ・ ! (album) ・ ! (disambiguation) ・ !! ・ !!! ・ !!! (album) ・ !!Destroy-Oh-Boy!! ・ !Action Pact! ・ !Arriba! La Pachanga ・ !Hero ・ !Hero (album) ・ !Kung language ・ !Oka Tokat ・ !PAUS3 ・ !T.O.O.H.! ・ !Women Art Revolution 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 Thomas algorithm ： ウィキペディア英語版 Tridiagonal matrix algorithm In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for ''n'' unknowns may be written as :$$ a_i x_ + b_i x_i + c_i x_ = d_i , \,\! where $a\_1\; =\; 0\backslash ,$ and $c\_n\; =\; 0\backslash ,$. :$$ \begin & & & & \\ & & & & \\ & & & \ddots & \\ & & \ddots & \ddots & & & & & \\ \end \begin \\ \\ \\ \vdots \\ \\ \end = \begin \\ \\ \\ \vdots \\ \\ \end . For such systems, the solution can be obtained in $O(n)$ operations instead of $O(n^3)$ required by Gaussian elimination. A first sweep eliminates the $a\_i$'s, and then an (abbreviated) backward substitution produces the solution. Examples of such matrices commonly arise from the discretization of 1D Poisson equation (e.g., the 1D diffusion problem) and natural cubic spline interpolation; similar systems of matrices arise in tight binding physics or nearest neighbor effects models. Thomas' algorithm is not stable in general, but is so in several special cases, such as when the matrix is diagonally dominant (either by rows or columns) or symmetric positive definite;〔 for a more precise characterization of stability of Thomas' algorithm, see Higham Theorem 9.12. If stability is required in the general case, Gaussian elimination with partial pivoting (GEPP) is recommended instead. ==Method== The forward sweep consists of modifying the coefficients as follows, denoting the new modified coefficients with primes: :$c\text{'}\_i\; =$ \begin \begin \cfrac & ; & i = 1 \\ \cfrac \end \, :$b\text{'}\_i\; =1\; \backslash qquad\; \backslash qquad\; \backslash qquad\; ;\; \backslash \; i\; =\; 1,\; 2,\; \backslash ldots,\; n$ and :$d\text{'}\_i\; =$ \begin \begin \cfrac & ; & i = 1 \\ \cfrac} & ; & i = 2, 3, \dots, n. \\ \end \end \, The solution is then obtained by back substitution: :$x\_n\; =\; d\text{'}\_n\backslash ,$ :$x\_i\; =\; d\text{'}\_i\; -\; c\text{'}\_i\; x\_\; \backslash qquad\; ;\; \backslash \; i\; =\; n\; -\; 1,\; n\; -\; 2,\; \backslash ldots,\; 1.$ 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「Tridiagonal matrix 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.