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Optimal parameter choice rule for filter-based regularization schemes

Author

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  • Sayana, K.J.
  • Reddy, G.D.

Abstract

In this article, we explore the further study of filter based schemes along with parameter choice rules and then apply to pseudo-differential operator equations and the analytic continuation problem. As we know that the stability of the regularization schemes depends on the regularization parameter and here we derive an a posteriori parameter choice rule which is best among all other parameter choice rules; and this parameter choice rule minimizes an upper bound of the approximation error ‖xα,δ−x†‖. Numerical experiments are also provided to validate the proposed theory.

Suggested Citation

  • Sayana, K.J. & Reddy, G.D., 2024. "Optimal parameter choice rule for filter-based regularization schemes," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    • Handle: RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004090
    DOI: 10.1016/j.amc.2024.128948
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    References listed on IDEAS

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    1. Xiong, Xiangtuan & Zhu, Liqin & Li, Ming, 2011. "Regularization methods for a problem of analytic continuation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 332-345.
    2. Reddy, G.D., 2019. "A class of parameter choice rules for stationary iterated weighted Tikhonov regularization scheme," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 464-476.
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