A Fixed-Point Discrepancy Approach to Tikhonov Regularization Parameter Selection

Maged Alkilayh

Journal of Mathematics, 2026, vol. 2026, 1-15

Abstract: This paper presents a unified comparative study of Tikhonov regularization parameter selection for linear ill-posed problems with both data noise and operator perturbations. We integrate the generalized discrepancy principle (GDP), its fixed-point formulation (GDP–FP), and the Arnoldi–Neubauer projection approach (PGDP–AN) within a common analytical and numerical framework that explicitly accounts for operator uncertainty and establishes monotone convergence of the fixed-point iterations under explicitly stated assumptions. Rather than proposing new individual selection rules, the contribution lies in a unified operator-aware analysis with complete proofs, a quantitative criterion for switching between data-dominated and operator-dominated formulations, and a reproducible benchmarking protocol with quantitative stability metrics. Numerical experiments on Baart’s integral equation, Gaussian image deblurring, inverse heat conduction, and inverse Laplace transform problems show that GDP–FP achieves high accuracy for smooth solutions, projection-based methods provide stability for large-scale problems, and PGDP–AN offers robustness under operator perturbations. The results clarify the strengths and limitations of each approach, providing a reproducible and theoretically grounded framework for parameter selection in inverse problems.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/7963108.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/7963108.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7963108

DOI: 10.1155/jom/7963108

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().