A simplified homotopy perturbation method for solving nonlinear ill-posed operator equations in Hilbert spaces
DOI:
https://doi.org/10.33993/jnaat541-1544Keywords:
Nonlinear ill-posed operator equations, Iterative regularization methods, Nonlinear operators on Hilbert spaces, Convergence analysis, Homotopy perturbation methodAbstract
One popular regularization technique for handling both linear and nonlinear ill-posed problems is homotopy perturbation. In order to solve nonlinear ill-posed problems, we investigate an iteratively-regularized simplified version of the Homotopy perturbation approach in this study. We examine the method's thorough convergence analysis under typical circumstances, focusing on the nonlinearity and the convergence rate under a H\"{o}lder-type source condition. Lastly, numerical simulations are run to confirm the method's effectiveness.
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Copyright (c) 2025 Sharad Kumar Dixit
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
