报告题目：Dual gradient flow for solving linear inverse problems in Banach spaces

报告时间：2023-06-21  10:00 - 11:00

报告人：王薇， 嘉兴学院

报告地点：理学院东北楼302

Abstract: In this talk, we consider determining the R-minimizing solution of ill-posed problem A x = y for a bounded linear operator A: X \to Y from a Banach space X to a Hilbert space Y, where R is a strongly convex function. A dual gradient flow is proposed to approximate the sought solution by using noisy data. Due to the ill-posedness of the underlying problem, the flow demonstrates the semi-convergence phenomenon and a stopping time should be chosen carefully to find reasonable approximate solutions. We consider the choice of a proper stopping time by various rules such as the a priori rules, the discrepancy principle, and the heuristic discrepancy principle and establish the respective convergence results. Furthermore, convergence rates are derived under the variational source conditions on the sought solution. Numerical results are reported to test the performance of the dual gradient flow for linear inverse problems.