Stationary Iterated Weight Tikhonov Methods For Solving Two Kinds Of Inverse Problems

The inverse problem of identifying an unknown source is ill-posed.The kind of problems are an important research field of mathematical physics inverse problem.Even if the solution of this kind of problems exist does not depend continuously on the data.This paper studies two kinds of ill-posed problems,including identification of unknown source in heat equation and identification of unknown source in Poisson equation of ill-posed problems,and studies how to structure their iterative regularization solutions.The main task is to put forward two different stationary iterated weight Tikhonov methods to construct regular solution of identifying an unknown source in heat equation and identifying an unknown source in Poisson equation respectively.We discuss the choice rule of the prior and posterior parameters,and give the corresponding error estimation.