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Block reflector : ウィキペディア英語版
Block reflector

"A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one."
* see abstract here http://locus.siam.org/SINUM/volume-25/art_0725014.html
It is built out of many elementary reflectors.
It is also referred to as a triangular factor, and is a triangular matrix and they are used in the Householder transformation.
A reflector Q belonging to \mathcal M_n(\R) can be written in the form :
Q = I -auu^T where I is the identity matrix for \mathcal M_n(\R) , a is a scalar and u belongs to \mathcal .
==LAPACK routines==
Here are some of the LAPACK routines that apply to block reflectors
* "
*larft" forms the triangular vector T of a block reflector H=I-VTVH.
* "
*larzb" applies a block reflector or its transpose/conjugate transpose as returned by "
*tzrzf" to a general matrix.
* "
*larzt" forms the triangular vector T of a block reflector H=I-VTVH as returned by "
*tzrzf".
* "
*larfb" applies a block reflector or its transpose/conjugate transpose to a general rectangular matrix.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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