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 - <p style="text-align: justify;">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.</p>