Abstract
Regularization is a method for providing a stable approximate solution to ill-posed operator equations, and it involves the regularization parameter which plays an important role in the convergence of the method. In this article, we propose a class of a posteriori parameter choice rules for filter-based regularization methods and establish the optimal rate of convergence \(O(\delta ^{\frac{\nu }{\nu +1}})\) from the proposed rules. We study these methods along with the proposed parameter choice rules in the context of pseudo-differential operator equations as well as the analytic continuation problem. The numerical implementation of the pseudo-differential operator equation and analytic continuation problem is discussed.
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Acknowledgements
I want to express my gratitude to the faculties and my colleagues at SRM University AP for their valuable and constructive suggestions during the planning and development of this research work.
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Sayana, K.J., Reddy, G.D. A class of a posteriori parameter choice rules for filter-based regularization schemes. Numer Algor (2024). https://doi.org/10.1007/s11075-024-01815-x
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DOI: https://doi.org/10.1007/s11075-024-01815-x
Keywords
- Ill-posed problems
- Regularization
- Filter functions
- Parameter choice rules
- Pseudo-differential operator
- Analytic continuation problem