Iterative regularization methods for ill-posed hammerstein type operator equation with monotone nonlinear part

Abstract

We considered a procedure for solving an ill-posed Hammerstein type operator equation KF (x) = y, by solving the linear equation Kz = y first for z and then solving the nonlinear equation F (x) = z. Convergence analysis is carried out by means of suitably constructed majorizing sequences. The derived error estimate using an adaptive method proposed by Perverzev and Schock (2005) in relation to the noise level and a stopping rule based on the majorizing sequences are shown to be of optimal order with respect to certain assumptions on F (x?), where x? is the solution of KF (x) = y.