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GMRES methods for the solution of least square problems

2018/07/04 14:13  点击:[]

报告人殷俊锋 (同济大学)

 

 : 2018年7月6日  10:30—11:30

 

 : 理科楼 LA106

 

 :The standard iterative method for solving large sparse least squares problems is the CGLS method, or its stabilized version, LSQR. We consider alternative methods using a mapping matrix and applying the generalized minimal residual (GMRES) method. We give a sufficient condition concerning B for the GMRES methods to give a least squares solution without breakdown for arbitrary b, for overdetermined, underdetermined, and possibly rank-deficient problems. We then give a convergence analysis of the GMRES methods as well as the CGLS method. Then, we propose using the robust incomplete factorization (RIF) for B. Finally, we show by numerical experiments on overdetermined and underdetermined problems that, for ill-conditioned problems, the GMRES methods with RIF give least squares solutions faster than the CGLS and LSQR methods with RIF, and are similar in performance to the reorthogonalized CGLS with RIF.

 

报告人简介:殷俊锋,同济大学数学系教授,博士生导师,风险管理研究所成员,上海市浦江人才计划入选者,同济大学优秀青年教师入选者,2010年中国数学会计算数学分会应用数值代数奖获得者;长期从事数值代数、并行计算和高性能计算方法等方面的研究,目前从事计算数学与科学工程学科交叉领域的探索性研究;主持和参与含3项国家自然科学基金在内的10余项国家级与省部级科研项目,在国际知名期刊上发表多篇高水平的学术论文。更多信息参见殷教授主页:http://math.tongji.edu.cn/Data/View/3853

 

学院联系人: 李寒宇

 

欢迎广大师生积极参与!

 

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