讲座预告：MULTIDIMENSIONAL TOTAL LEAST SQUARES PROBLEM WITHLINEAR EQUALITY CONSTRAINT

报告人：魏益民（复旦大学）

报告时间：2022年5月26日15:30

报告地点：腾讯会议ID：677-217-218

报告题目：MULTIDIMENSIONAL TOTAL LEAST SQUARES PROBLEM WITHLINEAR EQUALITY CONSTRAINT

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, anexplicit solution is firstly derived for the multidimensional TLSE problem, as well as the solvability conditions. With applying the perturbation theory of invariant subspace, the multidimensionalTLSE problem is proved equivalent to a multidimensional unconstrained weighed total least squaresproblem 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 minimumFrobenius norm, and their computable upper bounds are also provided to reduce the storage andcomputational cost. All these results are appropriate for the single right-hand-side case and themultidimensional total least squares problem, which are two especial cases of the multidimensionalTLSE problem. In numerical experiments, the multidimensional TLSE model is successfully appliedto color image deblurring and denoising for the first time, and the numerical results also indicate theeffectiveness of the condition numbers.

报告人简介：魏益民，复旦大学数学科学学院教授、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。

魏益民教授已在国际学术期刊发表论文一百余篇；并在Springe、科学出版社等出版了多部专著。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；担任国际学术期刊《Comput.Appl. Math》,《J. Appl. Math. Comput.》和《高校计算数学学报》的编委。