Journal of Optimization Theory and Applications

, Volume 171, Issue 1, pp 262–275 | Cite as

The Convergence Properties for Regularized Landweber Method

  • Caifang Wang


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.


Regularization Landweber Convergence properties Linear system 

Mathematics Subject Classification

65F22 65F10 47N10 49N45 



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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Maritime UniversityShanghaiChina

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