An Inverse and Derivative Free Regularized Iterative Scheme for Nonlinear ill-Posed Mootone Operators
Authors
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Department of Mathematics, Government Ambalapuzha College Alappuzha Kerala ,IN
D. Pradeep -
Department of Mathematics, University College Trivandrum Kerala ,INE. Shinelal
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Department of Mathematics, Sanatana Dharma College Alappuzha Kerala ,INV. Ananthalakshmi
DOI:
https://doi.org/10.18311/jims/2024/33334Keywords:
Nonlinear Ill-Posed Problems, Regularization, Iterative Method, Parameter Choice Rule.Abstract
In this paper, we consider an inverse and derivative-free regularized iterative scheme for solving nonlinear ill-posed problems involving monotone operators based on the contraction principle in the Hilbert space. We prove that the scheme converges to the Lavrentiev solution. The salient features of this scheme are: (i.) convergence analysis and desired convergence rate require only weaker assumptions compared to many assumptions used in the standard scheme in literature, (ii.) a parameter choice strategy that gives the same convergence rate as that of an priori method without using the source condition (iii.) computation of an optimal order regularization parameter O(δ 1/2) using the proposed parameter choice rule. Finally, we supply numerical examples to illustrate the proposed scheme. Further, we compare the numerical results of the proposed method with the standard method to demonstrate that our method achieves better computational output.
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Copyright (c) 2024 Pradeep D, Shinelal E, Ananthalakshmy V
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2024-04-11
Published 2024-07-01
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