On saturation of the discrepancy principle for nonlinear Tikhonov regularization in Hilbert spaces

2024/05/14 by Qinian Jin, Jin, Qinian
Mathematics · #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2405.08269

Abstract

In this paper we revisit the discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems in Hilbert spaces and provide some new and improved saturation results under less restrictive conditions, comparing with the existing results in the literature.

Related

• Analysis of the discrepancy principle for Tikhonov regularization under low order source conditions
• A priori parameter choice in Tikhonov regularization with oversmoothing\n penalty for non-linear ill-posed problems
• A new approach to source conditions in regularization with general residual term
• Optimal order conditions for filter based regularization methods, with applications to variants of the Tikhonov method
• Converse results, saturation and quasi-optimality for Lavrentiev\n regularization of accretive problems