The Convergence Properties for Regularized Landweber Method

Caifang Wang ()
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Caifang Wang: Shanghai Maritime University

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 1, No 13, 262-275

Abstract: 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; 65F22; 65F10; 47N10; 49N45 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0961-7

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