A revisit on Landweber iteration. (19th June 2020)

• Record Type: Journal Article
• Authors: Real, Rommel; Jin, Qinian
• Is Part Of: Inverse problems. Volume 36:Number 7(2020)
• Publication Date: 2020-06-19
• Subjects: Landweber iteration -- inverse problems -- convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab8bc4
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper we revisit the discrepancy principle for Landweber iteration for solving linear as well as nonlinear inverse problems in Banach spaces and prove a new convergence result which requires neither the Gâteaux differentiability of the forward operator nor the reflexivity of the image space. Therefore, we expand the applied range of the discrepancy principle for Landweber iteration to cover non-smooth ill-posed inverse problems and to handle the situation that the data is contaminated by various types of noise.