Iterative methods of gradient type of irregular operator equations (Q1571311)

The author examines a gradient method with projection onto a subspace. This method is designed to find an approximate solution to a nonlinear operator equation without any assumption on the regularity of the operator. It is shown that the trajectories of this method are attracted to a small neighborhood of the solution for small variations of the process parameters (even for their values lying beyond the convergence domain) and for small perturbations of the problem's operator.