Solution smoothness of ill-posed equations in Hilbert spaces: four concepts and their cross connections

DOI10.1080/00036811.2011.563736zbMath1272.47017OpenAlexW1986721792WikidataQ58256400 ScholiaQ58256400MaRDI QIDQ2903166

Jens Flemming

Publication date: 23 August 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2011.563736

zbMATH Keywords

variational inequalityHilbert spaceBanach spaceconvergence rateTikhonov regularizationlinear ill-posed problemdistance functionFenchel dualitysource conditionindex functionbenchmark functionapproximate source conditionapproximate variational inequalitymodifier function

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (8)

A converse result for Banach space convergence rates in Tikhonov-type convex regularization of ill-posed linear equations ⋮ Variational multiscale nonparametric regression: smooth functions ⋮ On variational regularization: finite dimension and Hölder stability ⋮ Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods ⋮ Elastic-net regularization versus ℓ ¹ -regularization for linear inverse problems with quasi-sparse solutions ⋮ A new interpretation of (Tikhonov) regularization ⋮ Convergence rates of first- and higher-order dynamics for solving linear ill-posed problems ⋮ Generalized Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces

Cites Work

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• A New Approach to Source Conditions in Regularization with General Residual Term
• Regularization in Hilbert space under unbounded operators and general source conditions
• On Converse and Saturation Results for Tikhonov Regularization of Linear Ill-Posed Problems
• Geometry of linear ill-posed problems in variable Hilbert scales
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• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• On the analysis of distance functions for linear ill-posed problems with an application to the integration operator inL²
• Range Inclusions and Approximate Source Conditions with General Benchmark Functions
• How general are general source conditions?
• Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators

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