A new class of accelerated iterative regularization schemes for linear ill-posed inverse problems

Title: A new class of accelerated iterative regularization schemes for linear ill-posed inverse problems

Speaker：Ye Zhang(Faculty of Mathematics, Chemnitz University of Technology,09107 Chemnitz, Germany)

Time: April 30th 10：00-12：00

Location：200-9, Sir Run Run Shaw Business Administration building

Abstract: In this talk I will introduce a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a linear vanishing damping term, which can be viewed not only as a extension of the asymptotical regularization, but also as a continuous analog of the Nesterov's acceleration scheme. New iterative regularization methods are derived from this continuous model in combination with damped symplectic numerical schemes. The regularization property as well as convergence rates and acceleration effects under the conventional source conditions of both continuous and discretized methods are proven.

The second part of my talk is concerned with the application of the newly developed accelerated iterative regularization methods with a posteriori stopping rule to the diffusion-based bioluminescence tomography, which is modeled as an inverse source problem in elliptic partial differential equations with both Dirichlet and Neumann boundary data.

Contact person：Xiaoliang Cheng（xiaoliangcheng@zju.edu.cn）