MULTI-PARAMETER TIKHONOV REGULARIZATION FOR LINEAR ILL-POSED OPERATOR EQUATIONS  

作　　者：Zhongying Chen Yao Lu Yuesheng Xu Hongqi Yang 

机构地区：[1]Department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou 510275, China [2]Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, USA

出　　处：《Journal of Computational Mathematics》2008年第1期37-55,共19页计算数学（英文）

基　　金：supported in part by the Natural Science Foundation of China under grants 10371137;the Foundation of Doctoral Program of National Higher Education of China under grant 20030558008;Guangdong Provincial Natural Science Foundation of China under grant 05003308;the Foundation of Zhongshan University Advanced Research Center;supported in part by the US National Science Foundation under grant CCR-0407476;National Aeronautics and Space Administration under Cooperative Agreement NNX07AC37A;the Natural Science Foundation of China under grants 10371122 and 10631080;the Education Ministry of the People's Republic of China under the Changjiang Scholar Chair Professorship Program through Zhongshan University

摘　　要：We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multiparameter regularization over the single parameter regularization.

关 键 词：Ill-posed problems Tikhonov regularization Multi-parameter regularization 

分 类 号：O221[理学—运筹学与控制论]