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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 Polynomial-time algorithm for approximating the volume of convex bodies ： ウィキペディア英語版 Polynomial-time algorithm for approximating the volume of convex bodies The paper is a joint work by Martin Dyer, Alan M. Frieze and Ravindran Kannan.〔 〕 The main result of the paper is a randomized algorithm for finding an $\backslash epsilon$ approximation to the volume of a convex body $K$ in $n$-dimensional Euclidean space by assuming the existence of a membership oracle. The algorithm takes time bounded by a polynomial in $n$, the dimension of $K$ and $1/\backslash epsilon$. The algorithm is a sophisticated usage of the so-called Markov chain Monte Carlo (MCMC) method. The basic scheme of the algorithm is a nearly uniform sampling from within $K$ by placing a grid consisting $n$-dimensional cubes and doing a random walk over these cubes. By using the theory of rapidly mixing Markov chains, they show that it takes a polynomial time for the random walk to settle down to being a nearly uniform distribution. ==References== 〔 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「Polynomial-time algorithm for approximating the volume of convex bodies」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.