Heuristic rule for non-stationary iterated Tikhonov regularization in Banach spaces. (29th August 2018)

• Record Type: Journal Article
• Authors: Zhang, Zhengqiang; Jin, Qinian
• Is Part Of: Inverse problems. Volume 34:Number 11(2018:Nov.)
• Publication Date: 2018-08-29
• Subjects: heuristic rule -- inverse problems -- nonstationary iterated Tikhonov regularization; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aad918
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper we propose a heuristic rule of Hanke–Raus type for non-stationary iterated Tikhonov regularization for solving ill-posed inverse problems in Banach spaces. This heuristic rule does not need any information on the noise level and is fully data driven. Under certain conditions on the noisy data, we obtain a convergence result. Various numerical simulations are provided to illustrate the efficiency of the proposed heuristic rule.