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 with applications （基于Householder变换的四元数矩阵实保结构算法）
报告时间：2015年6月1日（周一）上午10:00—11:30
报告地点：静远楼1506学术报告厅
Abstract: In many scientific problems, one needs to perform numerical computations involving quaternion matrices.As one of most frequently used basic tools, performing efficient and reliable algorithms of Householder transformations for quaternion matrices takes central role. In thispaper,we survey three different formsof Householder based transformations for quaternion matrices in theliterature,and propose a new form ofquaternion Householder based transformation.We propose real structure-preserving algorithms of these Householderbased transformations,which make theprocedure computationally more flexible andefficient.We compare thecomputation counts and assignment numbers of these algorithms.As applications, we apply these algorithmsfor the quaternion QRdecomposition,quaternion least squaresproblem, and quaternion bidiagonalization inthe quaternion SVD. Allthesefour real structure-preserving algorithms aremore efficient, comparing to thealgorithms which applyQuaternion Toolbox using quaternion arithmetics,or algorithms which directly performsreal Householder transformations onthe real representation of a quaternionmatrix.Among these fourreal structure-preserving algorithms,the most efficient ones arereal structure-preserving algorithms based onquaternion Householder reflection, and the new proposed Householder basedtransformation.
魏木生教授个人简介：
魏木生, 男, 1982年获南京大学学士学位，1986年获美国布朗大学博士学位，1986-1988年先后在Minnesota大学应用数学研究所(IMA)，Ohio州立大学，Michigan州立大学进行博士后研究， 1988-2008年在华东师范大学任教，为终身教授,博士生导师。2008年起为上海师范大学教授,博士生导师。1993年起获国务院特殊津贴，先后获国家教委“科学技术进步奖”三等奖(独立完成)，宝钢教育基金 “优秀教师奖”，上海市“科技进步奖”二等奖(独立完成)，上海市育才奖，上海市“自然科学奖”三等奖两次(独立完成)。
魏木生教授先后研究了散射问题，信号处理，最小二乘问题的扰动理论，子空间的扰动，广义逆的反序律，图像重构，反馈控制解耦问题等。在SIAM J. Applied Mathematics, IEEE Transactions on Signal Processing,SIAM J. Matrix Analysis Applications, Automatica等国际著名期刊上发表学术论文120余篇，出版专著3部。