On Tikhonov regularization in Banach spaces – optimal convergence rates results

DOI10.1080/00036810802555474zbMath1200.65040OpenAlexW1997722810WikidataQ58186809 ScholiaQ58186809MaRDI QIDQ3391812

Torsten Hein

Publication date: 13 August 2009

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

Full work available at URL: https://doi.org/10.1080/00036810802555474

zbMATH Keywords

convergence ratesinverse problemerror estimatesduality mappingBanach spaceTikhonov regularizationBregman distanceill-posed linear and nonlinear operator equations

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with linear operators (65J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (3)

Improved and extended results for enhanced convergence rates of Tikhonov regularization in Banach spaces ⋮ Modified Landweber Iteration in Banach Spaces—Convergence and Convergence Rates ⋮ The analysis study on nonlinear iterative methods for inverse problems

Cites Work

• Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
• Well posedness and convergence of some regularisation methods for non-linear ill posed problems
• A Lepskij-type stopping rule for regularized Newton methods
• Nonlinear iterative methods for linear ill-posed problems in Banach spaces
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Convergence rates for regularization of ill-posed problems in Banach spaces by approximate source conditions
• Convergence rates of convex variational regularization
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• The Lepskii principle revisited
• Error estimates for non-quadratic regularization and the relation to enhancement
• Regularization of ill-posed problems in Banach spaces: convergence rates

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