Secant-type iteration for nonlinear ill-posed equations in Banach space-Reference-Cited by-同舟云学术

Secant-type iteration for nonlinear ill-posed equations in Banach space

Published:2022-01-04 Issue:0 Volume:0 Page:
ISSN:1569-3945
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

George Santhosh¹^ORCID,Sreedeep C. D.²^ORCID,Argyros Ioannis K.³^ORCID

Affiliation:

1. Department of Mathematical and Computational Sciences , National Institute of Technology Karnataka , Mangaluru 575 025 , India

2. Department of Mathematics , Amrita Vishwa Vidyapeetham , Amrithapuri 690525 , India

3. Department of Mathematical Sciences , Cameron University , Lawton , OK 73505 , USA

Abstract

Abstract In this paper, we study secant-type iteration for nonlinear ill-posed equations involving 𝑚-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2021-0019/pdf

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