Iterative processes for nonlinear ill-posed operator equations in Banach spaces on the basis of finite-dimensional regularization of the Newton-Kantorovich method

A general approach to constructing iterative processes for nonlinear ill-posed operator equations in Banach spaces is proposed. This approach is based on the linearization of the original equation followed by the regularization with the use of the finite-dimensional Petrov-Galerkin approximation. Various aspects of practical implementation of the processes obtained are discussed.