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

• Published in: Mathematics and computers in simulation
• Main Authors: Grammont, Laurence, Vasconcelos, Paulo B.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-02-2024; Elsevier
• Subjects: Computational methods; Fredholm integral equations; Ill-posed problems; Inverse problems; Mathematics; Projection; Tikhonov regularization; Projection; Ill-posed problems; Computational methods; Inverse problems; Fredholm integral equations; Tikhonov regularization; Fredholm integral equations, Inverse problems, Ill-posed problems, Tikhonov regularization, Projection, Computational methods
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2024.02.010

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.