METHODS FOR SOLVING NONLINEAR ILL-POSED PROBLEMS BASED ON THE TIKHONOV-LAVRENTIEV REGULARIZATION an‎d ITERATIVE APPROXIMATION

A problem of constructing a stable approximate solution for a nonlinear irregular operator equation is investigated. For approximating solutions of the equations regularized by the Tikhonov-Lavrentiev methods, the Levenberg-Marquardt and Newton type processes are used, and the linear convergence rate and the Fej ́er property are proved. An asymptotic stop- ping rule of iterations is formulated that guarantees the regularizing properties of iterations and error estimate. Analogous questions are briefly discussed for the gradient methods.