A DISCRETIZING LEVENBERG-MARQUARDT SCHEME FOR SOLVING NONLIEAR ILL-POSED INTEGRAL EQUATIONS  

作　　者：Rong Zhang Hongqi Yang 

机构地区：[1]School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341004,China [2]Guangdong Province Key Laboratory of Computational Science,School of Computer Science and Engineering,Sun Yat-sen University,Guangzhou 510275,China

出　　处：《Journal of Computational Mathematics》2022年第5期686-710,共25页计算数学（英文）

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);the Foundation of Education Committee of Jiangxi,China(GJJ201436);National Natural Science Foundation of China under grants 11571386 and 11761010.

摘　　要：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.

关 键 词：The regularizing Levenberg-Marquardt scheme Multiscale Galerkin methods Nonlinear ill-posed problems Heuristic parameter choice rule Optimal convergence rate. 

分 类 号：O17[理学—数学]