Accumulating Householder transformations, revisited
Accumulating Householder transformations, revisited
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重新审视不断积累的家庭转变
DOI：
10.1145/1141885.1141886
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
F. V. Zee
中科院分区：
文献类型：
--
作者：
Thierry Joffrain;Tze Meng Low;E. Quintana;R. V. D. Geijn;F. V. Zee
提出了一个与 Householder 变换累积为单个正交变换（称为紧凑 WY 变换）相关的定理。它提供了此变换计算的简单特征，并提出了计算它的替代算法。它还提出了一种替代变换，即 UT 变换，它与紧凑的 WY 变换具有相同的效用，后者需要较少的计算并具有类似的稳定性特性。这种替代性转变于十多年前首次发布，但并未被社区注意到。
A theorem related to the accumulation of Householder transformations into a single orthogonal transformation known as the compact WY transform is presented. It provides a simple characterization of the computation of this transformation and suggests an alternative algorithm for computing it. It also suggests an alternative transformation, the UT transform, with the same utility as the compact WY Transform which requires less computation and has similar stability properties. That alternative transformation was first published over a decade ago but has gone unnoticed by the community.