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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 Incomplete Cholesky factorization ： ウィキペディア英語版 Incomplete Cholesky factorization In numerical analysis, an incomplete Cholesky factorization of a symmetric positive definite matrix is a sparse approximation of the Cholesky factorization. An incomplete Cholesky factorization is often used as a preconditioner for algorithms like the conjugate gradient method. The Cholesky factorization of a positive definite matrix ''A'' is ''A'' = ''LL'' * where ''L'' is a lower triangular matrix. An incomplete Cholesky factorization is given by a sparse lower triangular matrix ''K'' that is in some sense close to ''L''. The corresponding preconditioner is ''KK'' *. One popular way to find such a matrix ''K'' is to use the algorithm for finding the exact Cholesky decomposition, except that any entry is set to zero if the corresponding entry in ''A'' is also zero. This gives an incomplete Cholesky factorization which is as sparse as the matrix ''A''. == Algorithm == For $i$ from $1$ to $N$: :$$ L_ = \left( ^ } \right)^ :For $j$ from $i+1$ to $N$: ::$$ L_ = }\left( ^ } } \right) 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「Incomplete Cholesky factorization」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.