A modified iteratively regularized Landweber iteration method: Hölder stability and convergence rates-Reference-Cited by-同舟云学术

A modified iteratively regularized Landweber iteration method: Hölder stability and convergence rates

Published:2024-08-04 Issue: Volume: 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. Department of Mathematics , 30112 Indian Institute of Technology Roorkee , Roorkee 247667 ; and Defence Research and Development Organization, Near Metcalfe House, New Delhi 110054 India

2. Department of Mathematics , 30112 Indian Institute of Technology Roorkee , Roorkee 247667 , India

Abstract

Abstract In this paper, we formulate the modified iteratively regularized Landweber iteration method in Banach spaces to solve the inverse problems for which the forward operator may be smooth or non-smooth. We study the convergence analysis of the modified method for both the perturbed as well as unperturbed data by utilizing the Hölder stability estimates. In the presence of perturbed data, we terminate the method via a discrepancy principle and show that it is in fact a convergence regularization method that terminates within a few iterations. In the presence of unperturbed data, we show that the iterates converge to the exact solution. Additionally, we deduce the convergence rates in the presence of perturbed as well as unperturbed data. Finally, we discuss two inverse problems on which the method is applicable.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2023-0070/pdf

Reference34 articles.

1. G. S. Alberti and M. Santacesaria, Calderón’s inverse problem with a finite number of measurements, Forum Math. Sigma 7 (2019), Paper No. e35.

2. G. S. Alberti and M. Santacesaria, Calderón’s inverse problem with a finite number of measurements II: Independent data, Appl. Anal. 101 (2022), no. 10, 3636–3654.

3. G. S. Alberti and M. Santacesaria, Infinite-dimensional inverse problems with finite measurements, Arch. Ration. Mech. Anal. 243 (2022), no. 1, 1–31.

4. G. Alessandrini and S. Vessella, Lipschitz stability for the inverse conductivity problem, Adv. Appl. Math. 35 (2005), no. 2, 207–241.

5. I. K. Argyros and S. George, Unified convergence analysis of frozen Newton-like methods under generalized conditions, J. Comput. Appl. Math. 347 (2019), 95–107.