The Convergence Properties for Regularized Landweber Method

Landweber scheme is a widely used method to get a stable solution of linear system. The iteration of the Landweber scheme is viewed as a solution of normal equation for a least‐squares functional. However, in practice, regularized least‐squares functional is considered so as to get a more suitable solution. In this paper, we consider a regularized optimization problem and study the regularized Landweber scheme. Using the eigenvalue decomposition and the result that two symmetric semi‐positive definite matrices can be diagonalized simultaneously, we derive a presentation of the regularized Landweber scheme and then generate the convergence properties for the regularized Landweber iteration. Finally, we apply two‐dimensional numerical examples to confirm the convergence conditions.