An implicit Landweber method for nonlinear ill-posed operator equations

Authors:
Wei Wang;Bo Han
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we are interested in the solution of nonlinear inverse problems of the form F(x)=y. We propose an implicit Landweber method, which is similar to the third-order midpoint Newton method in form, and consider the convergence behavior of the implicit Landweber method. Using the discrepancy principle as a stopping criterion, we obtain a regularization method for ill-posed problems. We conclude with numerical examples confirming the theoretical results, including comparisons with the classical Landweber iteration and presented modified Landweber methods.