• AN ITERATIVE METHOD WITH QUADRATIC CONVERGENCE FOR NONLINEAR ILL-POSED PROBLEMS: FINITE-DIMENSIONAL REALIZATIONS

Abstract

An iterative regularization method which converges quadratically in the setting of a finite-dimensional subspace has been considered for obtaining stable approximate solution to nonlinear ill-posed operator equations The derived error estimate using an adaptive selection of the parameter in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill-posed-ness of the equation. A stopping rule for the iteration index is provided. The results of computational experiments are provided which shows the reliability of our method.