Optimal parameter choice rule for filter-based regularization schemes

K.J. Sayana and G.D. Reddy

Applied Mathematics and Computation, 2024, vol. 481, issue C

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.

Keywords: Ill-posed problems; Regularization; Filter functions; Parameter choice rules; Pseudo-differential operator; Analytic continuation problem (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:481:y:2024:i:c:s0096300324004090

DOI: 10.1016/j.amc.2024.128948

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