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A modified iterative Lavrentiev method for nonlinear monotone ill-posed operators

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Abstract

In this paper, we consider an iterative scheme for solving nonlinear ill-posed operator equations of monotone types under minimal and weaker assumptions. The convergence analysis of the scheme is carried out with both a priori and a posteriori parameter choice strategies and the error estimate is derived accordingly. Finally, we supply numerical examples to illustrate the proposed scheme by considering the model of nonlinear integral equations in Wiener-type filtering theory, and the efficiency of the proposed scheme is compared with other schemes.

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Acknowledgements

We profoundly thank the unknown referee(s) for their careful reading of the manuscript and valuable suggestions that significantly improved the presentation of the paper as well.

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Authors and Affiliations

  1. Department of Mathematics, Government College Ambalapuzha, Alappuzha, Kerala, 688561, India

    D. Pradeep

  2. School of Mathematics, Indian Institute of Science Education and Research Thiruvananthapuram, Vithura, Thiruvananthapuram, Kerala, 695551, India

    M. P. Rajan

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  1. D. Pradeep
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  2. M. P. Rajan
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Correspondence to D. Pradeep.

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Communicated by K. Sandeep.

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Pradeep, D., Rajan, M.P. A modified iterative Lavrentiev method for nonlinear monotone ill-posed operators. Indian J Pure Appl Math 55, 341–356 (2024). https://doi.org/10.1007/s13226-023-00368-4

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