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An improved Newton-type iteration method for regularizing the abstract nonlinear ill-posed operator equation is presented and also certain stopping criterion to determine the iteration is proposed in this paper by using the Newton-Landber iteration and the linear Tikhonov regularization. Under the condition that the Fréchet-derivation operator is uniformly boundary and further assumptions on the closeness and smoothness of the exact solution, the local convergence of the approximate solution is obtained. Keywords—nonlinear; ill-posed; operator equations; Newtontype method; convergence

The Convergence Analysis of an Improved Newton-type Method for the Regularization of Nonlinear Ill-Posed Problems