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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 Graver basis ： ウィキペディア英語版 Graver basis In applied mathematics, Graver bases enable iterative solutions of linear and various nonlinear integer programming problems in polynomial time. They were introduced by Jack E. Graver.〔Jack E. Graver: On the foundations of linear and linear integer programming, Mathematical Programming 9:207–226, 1975〕 Their connection to the theory of Gröbner bases was discussed by Bernd Sturmfels.〔Bernd Sturmfels, ''Gröbner Bases and Convex Polytopes'', American Mathematical Society, xii+162 pp., 1996〕 The algorithmic theory of Graver bases and its application to integer programming is described by Shmuel Onn.〔(Shmuel onn ): (''Nonlinear Discrete Optimization'' ), European Mathematical Society, x+137 pp., 2010〕〔Shmuel Onn: (Linear and nonlinear integer optimization ), Online Video Lecture Series, Mathematical Sciences Research Institute, Berkeley, 2010〕 ==Formal definition== The Graver basis of an ''m'' × ''n'' integer matrix $A$ is the finite set $G(A)$ of minimal elements in the set : $\backslash \; \backslash ,$ under a well partial order on $\backslash mathbb^n$ defined by $x\backslash sqsubseteq\; y$ when $x\_iy\_i\backslash geq\; 0$ and $|x\_i|\backslash leq\; |y\_i|$ for all i. For example, the Graver basis of $A=(1\; 2\; 1)$ consists of the vectors (2,−1,0), (0,−1,2), (1,0,−1), (1,−1,1) and their negations. 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「Graver basis」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.