154.com皇冠学术报告

A surrogate hyperplane Bregman-Kaczmarz method for solving linear inverse problems

殷俊锋 教授

（同济大学154.com皇冠）

报告时间：2024年5月31日 星期五 下午15：00-16：00

报告地点：腾讯会议：724-635-549 会议密码：0531

报告摘要：Linear inverse problems arise in many practical applications. In the present work, we propose a residual-based surrogate hyperplane Bregman-Kaczmarz method (RSHBK) for solving this kind of problems. The convergence theory of the proposed method is investigated detailedly. When the data is contaminated by the independent noise, an adaptive version of our RSHBK method is developed. An adaptive relaxation parameter is derived for optimizing the bound on the expectation error. It is proved that our adaptive RSHBK method converges to the true solution under certain conditions through the utilization of Lambert-W function. We demonstrate the efficiency of our proposed methods for both noise-free and independent noise problems by comparing with other state-of-the-art Kaczmarz methods in terms of computation time and convergence rate through synthetic experiments and real-world applications.

报告人简介：同济大学154.com皇冠教授，博导，主要研究方向数值代数与科学计算，计算金融，大数据和人工智能。主持及参与国家自然科学基金、上海市及教育部等科研项目10余项，发表高水平SCI学术论文30余篇，2009年入选上海市“浦江人才”,2010年荣获中国数学会计算数学分会应用数值代数奖，2019年获中国数学会计算数学分会青年创新奖（提名），现为中国工业与应用数学学会副秘书长，中国工业与应用数学学会大数据与人工智能专业委员会委员，中国高等教育学会教育数学委员会常务理事。

邀请人：谢家新