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An implicit Landweber method for nonlinear ill-posed operator equations

✍ Scribed by Wei Wang; Bo Han

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 455 KB
Volume: 230
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.12.016

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✦ Synopsis

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.

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