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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 Givens rotation ： ウィキペディア英語版 Givens rotation In numerical linear algebra, a Givens rotation is a rotation in the plane spanned by two coordinates axes. Givens rotations are named after Wallace Givens, who introduced them to numerical analysts in the 1950s while he was working at Argonne National Laboratory. == Matrix representation == A Givens rotation is represented by a matrix of the form :$G(i,\; j,\; \backslash theta)\; =$ \begin 1 & \cdots & 0 & \cdots & 0 & \cdots & 0 \\ \vdots & \ddots & \vdots & & \vdots & & \vdots \\ 0 & \cdots & c & \cdots & -s & \cdots & 0 \\ \vdots & & \vdots & \ddots & \vdots & & \vdots \\ 0 & \cdots & s & \cdots & c & \cdots & 0 \\ \vdots & & \vdots & & \vdots & \ddots & \vdots \\ 0 & \cdots & 0 & \cdots & 0 & \cdots & 1 \end where appear at the intersections th and th rows and columns. That is, the non-zero elements of Givens matrix are given by: :$\backslash begin$ g_ & &= c \\ g_ &= s \qquad \text \ i > j \end (sign of sine switches for ) The product represents a counterclockwise rotation of the vector in the plane of radians, hence the name Givens rotation. The main use of Givens rotations in numerical linear algebra is to introduce zeros in vectors or matrices. This effect can, for example, be employed for computing the QR decomposition of a matrix. One advantage over Householder transformations is that they can easily be parallelised, and another is that often for very sparse matrices they have a lower operation count. 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「Givens rotation」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.