Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems*This research is partially supported by NSFC grant 11971408 and NSFC/ANR joint program 51661135011/ ANR-16-CE40-0026-01. (8th March 2021)

• Record Type: Journal Article
• Authors: Fan, Bin; Xu, Chuanju
• Is Part Of: Inverse problems. Volume 37:Number 4(2021)
• Publication Date: 2021-03-08
• Subjects: nonlinear ill-posed problems -- inexact Newton regularization -- two-point gradient method -- steep descent -- minimal error; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abc270
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we propose an inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems. The basic idea of the proposed method is to linearize the equation around each outer iteration and subsequently apply a so-called two-point gradient method in the inner loop to accelerate the iterative process. Under suitable assumptions, we show that the iteration sequence generated by the proposed algorithm converges to a solution of the related problem in the noiseless situation. Furthermore, the stability and regularization properties of the proposed algorithm are analyzed in the noise-data case. Several numerical examples are provided to validate the theoretical results and to demonstrate the efficiency of the proposed method.