The authors consider the nonlinear ill-posed operator equation , where is injective and continuously Fréchet differentiable on its domain ; , are Hilbert spaces. They assume that there exists a solution of the equation, and that only noisy data satisfying are available. To iteratively compute an approximation to they replace the -th Newton step by the linearized equation
where . Since the linearized equation inherits the ill-posedness of the initial equation the authors apply a Tikhonov regularization with the initial guess , called the regularized Gauss-Newton method (IRGNM). The following problems are studied: Convergence of the IRGNM for exact data; IRGNM with discrepancy principle for nonlinear problems; Solving the linearized equation.