Parameter identification in partial differential equations (PDEs) is addressed through a total variation based regularization method. The inverse problem of reconstructing the source term from noisy data is discussed, emphasizing the need for regularization due to ill-posedness. Various regularization approaches like Tikhonov and iterative methods are compared, with a focus on Lavrentiev regularization for monotone problems. The study highlights numerical algorithms and inertial techniques for solving inclusion problems efficiently. Primal-dual splitting algorithms with inertial effects are explored, showcasing advancements in solving complex monotone inclusion problems.
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by Pankaj Gauta... at arxiv.org 03-08-2024
https://arxiv.org/pdf/2403.04557.pdfDeeper Inquiries