Iterative Regularization Methods For Two Kinds Of Ill-posed Problems

This paper studies the analytical continuation and time fractional diffusion equation with unknown source identification problems of ill posed problems,and how to construct the iterative regularization solutions.The analytic continuation problem is a kind of serious ill posed problem,and the time fractional diffusion equation with unknown source identification problem is a kind of mild ill posed problem.With the Landweber iterative regularization is slightly different,the main task is to put forward two different iterative regularization method to construct regular solution respectively(due to the ill posedness of different degrees),and theoretically given prior and posterior parameters choice rule,and proved stability and convergence of iterative format under the two parameter selection.Finally several examples to illustrate the feasibility and the effectiveness of the two iteration method.