Abstract
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.
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