A class of parameter choice rules for stationary iterated weighted Tikhonov regularization scheme

摘要

Regularization procedure involves the regularization parameter that plays a crucial role in the convergence analysis of the regularization scheme. Recently, Reddy (2017) has proposed two a posteriori parameter choice rules to choose the regularization parameter in the weighted Tikhonov regularization scheme. The primary purpose of this article is to introduce a class of parameter choice rules to choose the regularization parameter in the stationary iterated weighted Tikhonov (SIWT) regularization scheme and derive the optimal rate of convergence O(δj(α+1)1+j(α+1)) for a stationary iterated method based on these proposed rules. The numerical experiments support our theoretical results.