报告学者：Michiel E. Hochstenbach

报告者单位：Department of Mathematics and Computer Science, Eindhoven University of Technology

报告时间：2024年11月21日（周四）10:00-11:30

报告地点：7215会议室

报告摘要：We propose two new algebraic reconstruction techniques based on Kaczmarz's method that produce a regularized solution to noisy tomography problems. Tomography problems exhibit semiconvergence when iterative methods are employed, and the aim is therefore to stop near the semiconvergence point. Our approach is based on an error gauge that is constructed by pairing standard down-sweep Kaczmarz's method with its up-sweep version; we stop the iterations when this error gauge is minimal. The reconstructions of the new methods differ from standard Kaczmarz iterates in that our final result is the average of the stopped up- and down-sweeps. Even when Kaczmarz's method is supplied with an oracle that provides the exact error---and is therefore able to stop at the best possible iterate---our methods have a lower two-norm error in the vast majority of our test cases. In terms of computational cost, our methods are a little cheaper than standard Kaczmarz equipped with a statistical stopping rule.

报告学者简介：Michiel E. Hochstenbach，荷兰埃因霍温理工大学副教授，博士生导师。在荷兰乌得勒支大学分别获得硕士和博士学位，2003年在德国杜塞尔多夫大学从事博士后研究，曾任美国凯斯西储大学的助理教授和比利时布鲁塞尔大学的休假客座助理教授。Michiel E. Hochstenbach副教授是国际著名数学专家，在《SIAM Journal on Scientific Computing》、《Journal of Scientific Computing》、《SIAM Journal on Matrix Analysis and Applications》等国际数学与应用数学知名期刊上发表学术论文60余篇。