摘要 : In this paper, we propose an inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems. The basic idea of the proposed method is to linearize the equation around each outer iteration a... 展开 In this paper, we propose an inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems. The basic idea of the proposed method is to linearize the equation around each outer iteration and subsequently apply a so-called two-point gradient method in the inner loop to accelerate the iterative process. Under suitable assumptions, we show that the iteration sequence generated by the proposed algorithm converges to a solution of the related problem in the noiseless situation. Furthermore, the stability and regularization properties of the proposed algorithm are analyzed in the noise-data case. Several numerical examples are provided to validate the theoretical results and to demonstrate the efficiency of the proposed method. 收起