理学院学术报告20201119-(1)
发布人:何杰  发布时间:2020-11-19   浏览次数:10

不适定问题系列报告(一)

 

报告题目:Solving the ill-posed problems by dynamical system methods

 

报告人:刘继军

东南大学数学学院  教授

报告时间: 20201119 线上

 

摘要:There are several regularizing schemes for solving ill-posed problems, such as the Tikhonov regularization, iteration regularization and projection regularization. To ensure the efficiency of the regularizing schemes which aim to get the stable solutions, all these schemes should consider the issues of construction of the regularizing solution, choice strategies for regularizing parameters as well as the convergence rate for the regularizing solution. In this talk, we will introduce a regularizing scheme based on the dynamical system method, which is originally proposed by Prof. A. Ramm around 2000. The main arguments are to construct the regularizing solution in terms of the solution to an ODE system with time as the regularizing parameter. In principle, this scheme can solve either linear or nonlinear ill-posed problems with rigorous mathematical foundations. It is worthwhile to implement this scheme to concrete problems and check its numerical performances.


 

报告人介绍:刘继军,博士,东南大学二级教授,博士生导师,享受国务院政府特殊津贴专家。2009,12-2014,11任东南大学数学系主任、东南大学理学部副主任。现任中国工业与应用数学学会常务理事,全国大学生数学建模竞赛组委会委员,江苏省计算数学学会副理事长,东南大学丘成桐中心常务副主任。长期从事数学物理反问题、大规模科学计算和介质成像的数学理论和方法的研究。主持完成国家自然科学基金重大研究计划、面上项目、国际合作项目、天元基金、中国博士后科学基金、江苏省自然科学基金等项目的研究。已在SIAM J. Appl. Math., SIAM J. Sci. Comput., Inverse Problems, Science China Mathematics, J. Comput. Maths., J. Sci. Comput.等发表学术论文130余篇,在科学出版社出版学术专著2本。曾受中国NSFC、德国DAAD、韩国21Brain Project等资助赴国外开展合作研究。现任国际SCI刊物J. Inverse Ill-posed Problems编委。入选江苏省青蓝工程青年骨干教师、中青年学术带头人,江苏省333工程第三层次培养人选。获宝钢教育基金会全国优秀教师一等奖,作为主持人获江苏省教学成果一等奖,江苏省自然科学三等奖,教育部自然科学二等奖。