R-K type Landweber method for nonlinear ill-posed problems

In this paper we propose the R-K type Landweber iteration and investigate the convergence of the method for nonlinear ill-posed problem F ( x ) = y where F : H → H is a nonlinear operator between Hilbert space H. Moreover, for perturbed data with noise level δ we prove that the convergence rate is O ( δ 2 / 3 ) under appropriate conditions. Finally, the numerical performance of this R-K type Landweber iteration for a nonlinear convolution equation is compared with the Landweber iteration.