Finite-Dimensional Realization of Lavrentiev Regularization for Nonlinear Ⅲ-posed Equations

摘要

A finite-dimensional realization of the two-step Newton method is considered for obtaining an approximate solution (reconstructed signals) for the nonlinear ill-posed equation F(x) =f when the available data (noisy signal) is f~δ with f-f~δ≤S and the operator F is monotone. We derived an optimal-order error estimate under a general source condition on x_0 x, where x_0 is the initial approximation to the actual solution (signal) x. The choice of the regularization parameter is made according to the adaptive method considered by Pereverzev and Schock (2005). 2D visualization shows the effectiveness of the proposed method.