Journal of Optimization Theory and Applications

, Volume 171, Issue 1, pp 262–275

# The Convergence Properties for Regularized Landweber Method

Article

## Abstract

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.

## Keywords

Regularization Landweber Convergence properties Linear system

## Mathematics Subject Classification

65F22 65F10 47N10 49N45

## Notes

### Acknowledgments

The author thanks the referee for careful reading and the valuable comments. Caifang Wang was partially supported by National Natural Science Foundation of China (11401372) and a grant from Shanghai Municipal Commission for Science and Technology (13ZR1455500).

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