Summary
In this paper we investigate iterated Tikhonov regularization for the solution of nonlinear ill-posed problems. In the case of linear ill-posed problems it is well-known that (under appropriate assumptions) then-th iterated regularized solutions can converge likeO(δ22/(2n+1)), where δ denotes the noise level of the data perturbation. We give conditions that guarantee this convergence rate also for nonlinear ill-posed problems, and motivate these conditions by the mapping degree. The results are derived by a comparison of the iterated regularized solutions of the nonlinear problem with the iterated regularized solutions of its linearization. Numerical examples are presented.
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Supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung,project P-7869 PHY, and by the Christian Doppler Society
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Scherzer, O. Convergence rates of iterated Tikhonov regularized solutions of nonlinear III — posed problems. Numer. Math. 66, 259–279 (1993). https://doi.org/10.1007/BF01385697
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DOI: https://doi.org/10.1007/BF01385697