报告名称：Multidimensional Total Least Squares Problem with Linear Equality Constraints

主讲人：魏益民 教授

邀请人：莫长鑫  讲师

时间：2022年4月1日    14:30—15:30

地点：腾讯会议（ID：400 970 665）

主办单位：江南娱乐体育官网入口

报告摘要

Many recent data analysis models are mathematically characterized by a multidimensional total least squares problem with linear equality constraints (TLSE). In this paper, an explicit solution is firstly derived for the multidimensional TLSE problem, as well as the solvability conditions. With applying the perturbation theory of invariant subspace, the multidimensional TLSE problem is proved equivalent to a multidimensional unconstrained weighed total least squares problem in the limit sense. The Kronecker product-based formulae are also given for the normwise, mixed, and componentwise condition numbers of the multidimensional TLSE solution of minimum Frobenius norm, and their computable upper bounds are also provided to reduce the storage and computational cost. All these results are appropriate for the single right-hand-side case and the multidimensional total least squares problem, which are two especial cases of the multidimensional TLSE problem. In numerical experiments, the multidimensional TLSE model is successfully applied to color image deblurring and denoising for the first time, and the numerical results also indicate the effectiveness of the condition numbers.

 

专家简介

    魏益民，复旦大学江南娱乐体育官网入口的教授、计算数学专业的博士生导师，从事矩阵计算的理论和应用研究二十余年。1997年在复旦大学数学研究所获得理学博士学位，是上海市应用数学重点实验室的研究人员，曾获得上海市高校优秀青年教师和上海市“曙光”学者的称号；获得上海市自然科学三等奖。魏益民已在国际学术期刊发表论文一百余篇；并在科学出版社出版了三本著作和一本英语教材：《广义逆：理论与计算》（英）（王国荣、魏益民和乔三正，2004）；《数值线性代数及其应用》（英）(金小庆和魏益民，2004)；《偏微分方程数值解的有效条件数》（英）（李子才、黄宏财和魏益民等，2013）；《广义逆的符号模式》（卜长江和魏益民，2014）。魏益民曾主持国家自然科学基金、教育部博士点基金项目和973项目的子课题；目前正主持国家自然科学基金项目，担任国际学术期刊《Comput. Appl. Math.》和《J. Appl. Math. Comput.》和《高校计算数学学报》的编委。