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Simplified REGINN-IT method in Banach spaces for nonlinear ill-posed operator equations

  • Pallavi Mahale EMAIL logo and Farheen M. Shaikh
Published/Copyright: October 28, 2023

Abstract

In 2021, Z. Fu, Y. Chen and B. Han introduced an inexact Newton regularization (REGINN-IT) using an idea involving the non-stationary iterated Tikhonov regularization scheme for solving nonlinear ill-posed operator equations. In this paper, we suggest a simplified version of the REGINN-IT scheme by using the Bregman distance, duality mapping and a suitable parameter choice strategy to produce an approximate solution. The method is comprised of inner and outer iteration steps. The outer iterates are stopped by a Morozov-type stopping rule, while the inner iterate is executed by making use of the non-stationary iterated Tikhonov scheme. We have studied convergence of the proposed method under some standard assumptions and utilizing tools from convex analysis. The novelty of the method is that it requires computation of the Fréchet derivative only at an initial guess of an exact solution and hence can be identified as more efficient compared to the method given by Z. Fu, Y. Chen and B. Han. Further, in the last section of the paper, we discuss test examples to inspect the proficiency of the method.

MSC 2010: 65J20; 65J22; 47J06

Award Identifier / Grant number: MTR/2019/000670

Funding statement: The first author acknowledges Science and Engineering Research Board (SERB), Department of Science & Technology, Government of India for the support for the work through MATRICS project file no. MTR/2019/000670, dated 11 February, 2020.

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Received: 2023-05-15
Revised: 2023-08-10
Accepted: 2023-08-28
Published Online: 2023-10-28
Published in Print: 2024-08-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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