深圳大学四十周年校庆暨数学学科四十周年庆

荔园杰出学者讲座第八期

讲座题目：A Uniform Preconditioner for a Newton Algorithm for Total-Variation Minimization and Minimum-Surface Problems

主讲人：TAI Xue Cheng教授（香港浸会大学）

讲座时间：2023年4月27日16:00-17:00

讲座地点：汇星楼金融科技学院教室3号报告厅

邀请人：数学与统计学院

内容概述：Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many efficient algorithms have been proposed. First order methods are common. They are popular due to their simplicity and easy implementation. Some second order Newton-type iterative methods have been proposed like Chan-Golub-Mulet method. In this talk, we will propose a new Newton-Krylov solver for primal-dual finite element discretization of the ROF model. The method is so simple that we just need to use some diagonal preconditioners during the iterations. Theoretically, the proposed preconditioners are further proved to be robust and optimal with respect to the mesh size, the penalization parameter, the regularization parameter, and the iterative step, essentially it is a parameter independent preconditioner. We first discretize the primal-dual system by using mixed finite element methods, and then linearize the discrete system by Newton’s method. Exploiting the well-posedness of the linearized problem on appropriate Sobolev spaces equipped with proper norms, we propose block diagonal preconditioners for the corresponding system solved with the minimum residual method. Numerical results are presented to support the theoretical results.

主讲人简介：台雪成教授于1991年在芬兰于韦斯屈莱大学获得博士学位。现为香港浸会大学理学院数学系系主任、教授。台教授长期从事数值数学和计算数学等方面的研究。台教授使用偏微分方程的数值方法和技巧来解决图像处理和数据分类方面的问题，并推广这些技术到其他现代应用。台教授于2001年获得新加坡南洋理工大学研究卓越奖；2009年获得第八届“冯康科学计算奖”。现担任 SIAM Journal on Imaging Sciences、Journal of Mathematical Imaging and Vision、Inverse Problems and Imaging、Journal of Information and Computing Science等期刊编委。

欢迎师生参加！

                                        数学与统计学院

                                                2023年04月23日