The analysis of a discrete scheme of the iteratively regularized Gauss-Newton method

In this paper, the iteratively regularized Gauss-Newton method is applied to compute the stable solutions of nonlinear inverse problems. For the numerical realization, the discretization of this method is considered and the iterative solution is used to approximate the exact solution. An a posteriori rule is suggested to choose the stopping index of iteration and the convergence and rates of convergence are also derived under certain conditions. An example from the parameter identification of a differential equation problem is given to illustrate the required conditions.