Convergence analysis of inexact Newton–Landweber iteration under Hölder stability. (1st January 2023)

• Record Type: Journal Article
• Authors: Xia, Yuxin; Han, Bo; Fu, Zhenwu
• Is Part Of: Inverse problems. Volume 39:Number 1(2023)
• Publication Date: 2023-01-01
• Subjects: nonlinear inverse problems -- Hölder stability estimate -- inexact Newton-Landweber iteration -- convergence -- convergence rate; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aca49d
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we focus on a class of inverse problems with Lipschitz continuous Fréchet derivatives both in Hilbert spaces and Banach spaces. The convergence and convergence rate of the inexact Newton–Landweber method (INLM) for such problems are presented under some assumptions. For the inverse problems in Hilbert spaces, we revisit the convergence result and the convergence rate of the INLM under Lipschitz condition and Hölder stability. Furthermore, the INLM for nonlinear inverse problems in Banach spaces is also considered. By using a Hölder stability corresponding to the Bregman distance, we derive the convergence property and convergence rate of the method.