报告题目：Statistical Condition Estimates and Randomized Algorithms for Large-Scale Total Least Squares Problems

报告人：魏益民教授

报告时间：2018年11月9日上午9:30

报告地点：数计学院4号楼229会议室

报告摘要：Motivated by the recently popular probabilistic methods for low-rank approximations and randomized algorithms for the least squares problems, we develop randomized algorithms for the total least squares (TLS) problem with a single right-hand side. We present the Nystr¨om method (NTLS) for the medium-sized problems. For the large-scale and ill-conditioned cases we introduce the randomized truncated Tls (Rttls) with the known or estimated rank as regularization parameter. We analyze the accuracy of the algorithm Rttls, and perform numerical experiments to demonstrate the efficiency of our randomized algorithms. The randomized algorithms can greatly reduce the computational time and still maintain good accuracy with very high probability. Under the genericity condition, we study the condition estimation of the total least squares (TLS) problem based on small sample condition estimation (SCE), which can be incorporated into the direct solver for the TLS problem via the singular value decomposition (SVD) of the augmented matrix [A, b]. Our proposed condition estimation algorithms are efficient for the small and medium size TLS problem because they utilize the computed SVD of [A, b] during the numerical solution to the TLS problem. Numerical examples illustrate the reliability of the algorithms. Both normwise and componentwise perturbations are considered. Moreover, structured condition estimations are investigated for the structured TLS problem.

报告人简介：魏益民教授,1997年毕业于复旦大学数学研究所并获得理学博士学位。毕业后留校在数学科学学院工作,2006年4月晋升正教授,计算数学专业博士生导师。2000.9-2001.6访问美国哈佛大学和麻省理工学院,任高访学者； 2008 年荣获“上海高校优秀青年教师”称号；2008年入选上海市‘曙光’学者。现为国际线性代数学会(ILAS) 会员、美国数学会会员、美国工业与应用数学会(SIAM) 会员、中国计算数学学会—线性代数专业委员会委员会员，美国数学评论评论员。同时担任Linear Algebra and its Applications， FILOMAT，高校计算数学学报等多个杂志的编委。

已在国际国内学术刊物上发表论文250余篇，与他人合作出版著作《Generalized Inverses: Theory and Computations》(科学出版社， 2004年)和英文教材《Numerical Linear Algebra and its Applications》(科学出版社， 2004 年)。