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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 Preconditioner ： ウィキペディア英語版 Preconditioner In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. == Preconditioning for linear systems == In linear algebra and numerical analysis, a preconditioner $P$ of a matrix $A$ is a matrix such that $P^A$ has a smaller condition number than $A$. It is also common to call $T=P^$ the preconditioner, rather than $P$, since $P$ itself is rarely explicitly available. In modern preconditioning, the application of $T=P^$, i.e., multiplication of a column vector, or a block of column vectors, by $T=P^$, is commonly performed by rather sophisticated computer software packages in a matrix-free fashion, i.e., where neither $P$, nor $T=P^$ (and often not even $A$) are explicitly available in a matrix form. Preconditioners are useful in iterative methods to solve a linear system $Ax=b$ for $x$ since the rate of convergence for most iterative linear solvers increases as the condition number of a matrix decreases as a result of preconditioning. Preconditioned iterative solvers typically outperform direct solvers, e.g., Gaussian elimination, for large, especially for sparse, matrices. Iterative solvers can be used as matrix-free methods, i.e. become the only choice if the coefficient matrix $A$ is not stored explicitly, but is accessed by evaluating matrix-vector products. 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「Preconditioner」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.