翻訳と辞書 Words near each other ・ Symbolab ・ Symbole ・ Symboli Kris S ・ Symboli Rudolf ・ Symbolia ・ Symbolic ・ Symbolic (Death album) ・ Symbolic (Voodoo Glow Skulls album) ・ Symbolic annihilation ・ Symbolic anthropology ・ Symbolic artificial intelligence ・ Symbolic behavior ・ Symbolic boundaries ・ Symbolic capital ・ Symbolic chickens ・ Symbolic Cholesky decomposition ・ Symbolic circuit analysis ・ Symbolic communication ・ Symbolic computation ・ Symbolic convergence theory ・ Symbolic culture ・ Symbolic data analysis ・ Symbolic dynamics ・ Symbolic ethnicity ・ Symbolic execution ・ Symbolic Gesture ・ Symbolic integration ・ Symbolic Interaction (journal) ・ Symbolic interactionism ・ Symbolic linguistic representation 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 Symbolic Cholesky decomposition ： ウィキペディア英語版 Symbolic Cholesky decomposition In the mathematical subfield of numerical analysis the symbolic Cholesky decomposition is an algorithm used to determine the non-zero pattern for the $L$ factors of a symmetric sparse matrix when applying the Cholesky decomposition or variants. ==Algorithm== Let $A=(a\_)\; \backslash in\; \backslash mathbb^$ be a sparse symmetric positive definite matrix with elements from a field $\backslash mathbb$, which we wish to factorize as $A\; =\; LL^T\backslash ,$. In order to implement an efficient sparse factorization it has been found to be necessary to determine the non zero structure of the factors before doing any numerical work. To write the algorithm down we use the following notation: * Let $\backslash mathcal\_i$ and $\backslash mathcal\_j$ be sets representing the non-zero patterns of columns and (below the diagonal only, and including diagonal elements) of matrices and respectively. * Take $\backslash min\backslash mathcal\_j$ to mean the smallest element of $\backslash mathcal\_j$. * Use a parent function $\backslash pi(i)\backslash ,\backslash !$ to define the elimination tree within the matrix. The following algorithm gives an efficient symbolic factorization of : : $$ \begin & \pi(i):=0~\mbox~i\\ & \mbox~i:=1~\mbox~n\\ & \qquad \mathcal_i := \mathcal_i\\ & \qquad \mbox~j~\mbox~\pi(j) = i\\ & \qquad \qquad \mathcal_i := (\mathcal_i \cup \mathcal_j)\setminus\\\ & \qquad \pi(i) := \min(\mathcal_i\setminus\) \end 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「Symbolic Cholesky decomposition」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.