George, Santhosh and Shobha, Monnanda Erappa (2013) Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations. Journal of Applied Mathematics and Computing , 41. ISSN 1598-5865

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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 x0. A numerical example of nonlinear integral equation shows the efficiency of this procedure

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