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复旦大学魏益民教授报告会

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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,复旦大学  

报告时间:2018年11月9日上午9:00—10:30

报告地点:数计学院4号楼229会议室

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)。