Real structure-preserving algorithms of Householder based transformations for quaternion matrices
Real structure-preserving algorithms of Householder based transformations for quaternion matrices
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DOI：
10.1016/j.cam.2016.03.031
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
Ying Li;M. Wei;Fengxia Zhang;Jianli Zhao
中科院分区：
文献类型：
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作者：
Ying Li;M. Wei;Fengxia Zhang;Jianli Zhao
本文综述了现有四元数矩阵的三种不同形式的基于Household的变换，并提出了一种新的基于Household的四元数变换形式。我们提出了这些基于Household的变换的实结构保持算法，使得该过程在计算上更加灵活和高效。我们对这些算法的计算量和分配次数进行了比较。我们还比较了这些保实结构算法在四元数QRD和四元数SVD上的有效性，这四种保实结构算法都比使用四元数算法的四元数工具箱算法或直接对四元数矩阵的实数表示执行实数Household变换的算法更有效。在这四种实数结构保持算法中，效率最高的是基于四元数的Household反射算法和新提出的基于Household变换的算法。
In this paper, we survey three different forms of Householder based transformations for quaternion matrices in the literature, and propose a new form of quaternion Householder based transformation. We propose real structure-preserving algorithms of these Householder based transformations, which make the procedure computationally more flexible and efficient. We compare the computation counts and assignment numbers of these algorithms. We also compare the effectiveness of these real structure-preserving algorithms applying to the quaternion QRD and the quaternion SVD.All these four real structure-preserving algorithms are more efficient, comparing to the algorithms which apply Quaternion Toolbox using quaternion arithmetics, or algorithms which directly performs real Householder transformations on the real representation of a quaternion matrix. Among these four real structure-preserving algorithms, the most efficient ones are based on quaternion Householder reflection, and new proposed Householder based transformation.