Some Newton-type methods for the regularization of nonlinear ill-posed problems
- 1 June 1997
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 13 (3), 729-753
- https://doi.org/10.1088/0266-5611/13/3/012
Abstract
In this paper we consider a combination of Newton's method with linear Tikhonov regularization, linear Landweber iteration and truncated SVD, for regularizing an abstract, nonlinear, ill-posed operator equation. We show that under certain smoothness conditions on the nonlinear operator, these methods converge locally. For perturbed data we propose an a priori stopping rule, that guarantees convergence of the iterates to a solution, as the noise level goes to zero. Under appropriate closeness and smoothness assumptions on the starting value and the solution, we obtain convergence rates.Keywords
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