To reduce the computational cost,we propose a regularizing modified LevenbergMarquardt scheme via multiscale Galerkin method for solving nonlinear ill-posed problems.Convergence results for the regularizing modified L...To reduce the computational cost,we propose a regularizing modified LevenbergMarquardt scheme via multiscale Galerkin method for solving nonlinear ill-posed problems.Convergence results for the regularizing modified Levenberg-Marquardt scheme for the solution of nonlinear ill-posed problems have been proved.Based on these results,we propose a modified heuristic parameter choice rule to terminate the regularizing modified Levenberg-Marquardt scheme.By imposing certain conditions on the noise,we derive optimal convergence rates on the approximate solution under special source conditions.Numerical results are presented to illustrate the performance of the regularizing modified Levenberg-Marquardt scheme under the modified heuristic parameter choice.展开更多
基金Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(2020B1212060032)Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques(400440)+1 种基金the Foundation of Education Committee of Jiangxi,China(GJJ201436)National Natural Science Foundation of China under grants 11571386 and 11761010.
文摘To reduce the computational cost,we propose a regularizing modified LevenbergMarquardt scheme via multiscale Galerkin method for solving nonlinear ill-posed problems.Convergence results for the regularizing modified Levenberg-Marquardt scheme for the solution of nonlinear ill-posed problems have been proved.Based on these results,we propose a modified heuristic parameter choice rule to terminate the regularizing modified Levenberg-Marquardt scheme.By imposing certain conditions on the noise,we derive optimal convergence rates on the approximate solution under special source conditions.Numerical results are presented to illustrate the performance of the regularizing modified Levenberg-Marquardt scheme under the modified heuristic parameter choice.
