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

摘要

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(δ2/3) 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.