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A class of a posteriori parameter choice rules for filter-based regularization schemes

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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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Authors and Affiliations

  1. Department of Mathematics, SRM University AP, Neerukonda, Amaravati, Andhra Pradesh, 522502, India

    K. J. Sayana & G. D. Reddy

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  1. K. J. Sayana
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  2. G. D. Reddy
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The two authors contributed equally to the preparation of this article.

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Correspondence to G. D. Reddy.

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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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