mg真人娱乐网站学术报告: Real structure-preserving algorithms of Householder based transformations for quaternion matrices

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

时间:2018年5月18日(周五) 16:00

地点:7JC306

主讲人:魏木生

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.

主讲人概况:

魏木生,上海师范大学数理学院教授,博士生导师,聊城大学特聘教授。原华东师范大学数学系教授,博士生导师,终身教授。享受国务院政府特殊津贴,并先后获得过国家教委科技进步奖、宝钢教育基金优秀教师奖、上海市科技进步奖,上海市育才奖和上海市自然科学奖(两项)。魏教授主持国家自然科学基金六项,主持国家教委优秀年轻教师基金一项,主持上海市科委基础研究重点项目基金一项,并参加美国自然科学基金,美国海军研究基金,巴西圣保罗州研究基金,加拿大自然科学基金项目。

魏教授研究了偏微分方程的散射问题和散射频率的计算,指数型非线性信号的参数辩识,秩亏LS、TLS和LSE问题的理论和扰动分析和数值计算,刚性最小二乘问题的上确界,稳定性扰动和算法研究,矩阵乘积的广义逆的反序律,图像重构,控制论中的系统的标准分解和对角解耦,谱范数下矩阵逼近问题的极小秩解,四元数矩阵计算和彩色图像处理等问题。

魏教授已在国内外知名刊物发表学术论文150余篇;出版书籍:《Supremum and Stability of Weighted Pseudoinverses and Weighted Least Squares Problems: Analysis and Computations》(Nova Science Publishers, New York, 2001),《数学分析习题精解》(科学出版社,北京,2002),《广义最小二乘问题的理论和计算》(科学出版社,北京,2006),《奇异值分解及其在广义逆理论中的应用》(科学出版社,北京,2008)。现在正在撰写英文专著《Quaternion Matrix Computations》。

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