A priori parameter choice in Tikhonov regularization with oversmoothing\n penalty for non-linear ill-posed problems

2019/04/03 by Bernd Hofmann, Hofmann, Bernd, Peter Mathé +1
Mathematics · #65J20 #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #primary 65J22 #secondary47J06

paper · pdf · doi:10.48550/arxiv.1904.02014

openalex publication_date 2019/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Tikhonov regularization for certain classes of non-linear ill-posed\noperator equations in Hilbert space. Emphasis is on the case where the solution\nsmoothness fails to have a finite penalty value, as in the preceding study\n'Tikhonov regularization with oversmoothing penalty for non-linear ill-posed\nproblems in Hilbert scales'. Inverse Problems 34(1), 2018, by the same authors.\nOptimal order convergence rates are established for the specific a priori\nparameter choice, as used for the corresponding linear equations.\n

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