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A convergence analysis of the Landweber iteration for nonlinear ill-posed problems

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In this paper we prove that the Landweber iteration is a stable method for solving nonlinear ill-posed problems. For perturbed data with noise level \(\delta \) we propose a stopping rule that yields the convergence rate\(O (\delta ^{1/2}\) ) under appropriate conditions. We illustrate these conditions for a few examples.

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Received February 15, 1993 / Revised version received August 2, 1994

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Hanke, M., Neubauer, A. & Scherzer, O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems . Numer Math 72, 21–37 (1995). https://doi.org/10.1007/s002110050158

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  • DOI: https://doi.org/10.1007/s002110050158

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