George, S.Erappa, M.E.2026-02-052014Journal of Applied Mathematics and Computing, 2014, 44, 46054, pp. 69-8215985865https://doi.org/10.1007/s12190-013-0681-1https://idr.nitk.ac.in/handle/123456789/26532An 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.Adaptive choiceGauss-Newton methodsHammersteinIterative regularizationNonlinear ill-posed problemsTikhonov regularizationMathematical operatorsNewton-Raphson methodProblem solving