Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations
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Date
2014
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Abstract
An iterative method is investigated for a nonlinear ill-posed Hammerstein type operator equation KF(x)=f. We use a center-type Lipschitz condition in our convergence analysis instead of the usual Lipschitz condition. The adaptive method of Pereverzev and Schock (SIAM J. Numer. Anal. 43(5):2060-2076, 2005) is used for choosing the regularization parameter. The optimality of this method is proved under a general source condition involving the Fréchet derivative of F at some initial guess x <inf>0</inf>. A numerical example of nonlinear integral equation shows the efficiency of this procedure. © 2013 Korean Society for Computational and Applied Mathematics.
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Keywords
Adaptive choice, Gauss-Newton methods, Hammerstein, Iterative regularization, Nonlinear ill-posed problems, Tikhonov regularization, Mathematical operators, Newton-Raphson method, Problem solving
Citation
Journal of Applied Mathematics and Computing, 2014, 44, 46054, pp. 69-82