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