报 告 人：魏木生 教授（上海师范大学 ）

报告题目：Real structure-preserving algorithms of Householder based transformations for quaternion matrices

报告时间：2016年5月20日上午10：00

报告地点：静远楼204会议室

报告摘要：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.