On ill-posedness concepts, stable solvability and saturation

DOI10.1515/jiip-2017-0090zbMath1492.47019arXiv1709.01109OpenAlexW2964236274MaRDI QIDQ1746506

Bernd Hofmann, Robert Plato

Publication date: 25 April 2018

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.01109

zbMATH Keywords

regularizationill-posednesssaturationoperator equationsstable solvabilitylinear and nonlinear inverse problems

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (11)

Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions ⋮ On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case ⋮ Case Studies and a Pitfall for Nonlinear Variational Regularization Under Conditional Stability ⋮ Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term ⋮ Tikhonov regularization in Hilbert scales under conditional stability assumptions ⋮ Two new non-negativity preserving iterative regularization methods for ill-posed inverse problems ⋮ Convergence analysis of (statistical) inverse problems under conditional stability estimates ⋮ A regularized variational inequality approach for nonlinear monotone ill-posed equations ⋮ Generalized Lavrentiev-type regularization method for the Cauchy problem of a semi-linear elliptic equation ⋮ Simultaneous identification of volatility and interest rate functions -- a two-parameter regularization approach ⋮ Oversmoothing Tikhonov regularization in Banach spaces ^*

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