| Nowadays the methods studied for nonlinear ill-posed problems are Tikhonov-regularization and iterative regularized methods. In order to obtain the convergence of iterative regularized methods, one has to imposed rather stiingent conditions on the operator and its Frechet derivative. However, for practical applications, it is difficult to prove the required conditions. But as to Tikhonov- regularization, we obtain the convergence under mild restrictions on the nonlinear operator. However, one usually encounters two problems when using Tikhonov- regularization: firstly, how to find a proper regularization parameter and secondly, how to compute the global minimizer of the Tikhonov- regularization.In this paper, for conditions twice Frechet-differentiable operator equations with Lipschitz conditions first derivative, like Tikhonov-regularization, and using the thought of homotopy, we present a functional and take the global minimizer of the functional as one approximate of the solution of the nonlinear ill-posed problems. We take LM method to compute the minimizer of the function. Theory and numerical simulation show that the method presented is a convergence and stable method. |
