TY - JOUR T1 - Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations JO - Journal of Computational Mathematics VL - 1 SP - 37 EP - 55 PY - 2008 DA - 2008/02 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8609.html KW - Ill-posed problems, Tikhonov regularization, Multi-parameter regularization. AB -
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 multi-parameter regularization over the single parameter regularization.