Influence of the order between discretization and regularization in solving ill-posed problems

Laurence Grammont and Paulo B. Vasconcelos

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 230, issue C, 400-412

Abstract: Discretization and regularization are required steps to provide a stable approximation when solving integral equations of the first kind. The integral operator involved may be approximated by a sequence of finite rank operators and then the regularization procedure is applied. On the other hand, a regularization procedure can be conceived prior to the discretization. Both approaches are developed, implemented and compared for certain projection based methods.

Keywords: Fredholm integral equations; Inverse problems; Ill-posed problems; Tikhonov regularization; Projection; Computational methods (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:230:y:2025:i:c:p:400-412

DOI: 10.1016/j.matcom.2024.02.010

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