On the iterated Tikhonov regularization for ill-posed problems

The iterated Tikhonov regularization for solving ill-posed problems is considered: x0α=0,(αI+K*K)xmα=K*y+αxm-1α,m=1,2,… The parameter m plays the role of the regularization parameter when the parameter α0 is fixed in this method.we deduce the property of regularizing filter function,give a priori optimal choice of m(α,δ)=O(αδ-2 2r+1),r≥0 and obtain optimal order of convergence.In practice,it is more convenient than viewing α as the regularization parameter for computation.Finally,a numerical example is included to verify the theoretical results.