Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces-Reference-Cited by-同舟云学术

Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces

Published:2023-06-27 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Mittal Gaurav¹,Giri Ankik Kumar²

Affiliation:

1. Defence Research and Development Organization , New Delhi , 110054 ; and Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667 , India

2. Department of Mathematics , Indian Institute of Technology Roorkee , Roorkee , 247667 , India

Abstract

Abstract In this paper, we study the convergence analysis of the inexact Newton–Landweber iteration method (INLIM) with frozen derivative in Hilbert as well as Banach spaces. To study the convergence analysis, we incorporate the Hölder stability of the inverse mapping and Lipschitz continuity of the Fréchet derivative of the forward mapping. Moreover, we derive the convergence rates of INLIM in Hilbert as well as Banach spaces without using any extra smoothness condition. Finally, we compare our convergence rates results with that of several other frozen methods proposed in the literature to solve inverse problems.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2023-0002/pdf

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