A convergence analysis of an inexact Newton-Landweber iteration method for nonlinear problem. Issue 7 (19th May 2018)

• Record Type: Journal Article
• Authors: Wang, Ying; Li, Jing; Wang, Jinping
• Is Part Of: Applicable analysis. Volume 97:Issue 7(2018)
• Page Start: 1106
• Page End: 1116
• Publication Date: 2018-05-19
• Subjects: Nonlinear problem -- convergence rates -- the Newton–Landweber iteration -- Hölder-type stability; 65R20 -- 68W25 -- 65F22; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1300793
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the convergence and the convergence rates of an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. Opposed to the traditional methods, we analyze an inexact Newton–Landweber iteration depending on the Hölder continuity of the inverse mapping when the data are not contaminated by noise. With the namely Hölder-type stability and the Lipschitz continuity of DF, we prove convergence and monotonicity of the residuals defined by the sequence induced by the iteration. Finally, we discuss the convergence rates.