Regularization in Banach spaces — convergence rates by approximative source conditions

DOI10.1515/JIIP.2009.004zbMath1167.65024MaRDI QIDQ3612229

Torsten Hein

Publication date: 3 March 2009

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

zbMATH Keywords

convergence ratesregularizationreflexive Banach spaceserror boundill-posed problembounded linear operatordistance functionnonlinear operatorsa-posteriori parameter choice method

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)

Related Items (1)

Modified Landweber Iteration in Banach Spaces—Convergence and Convergence Rates

Cites Work

• Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
• Morozov's discrepancy principle under general source conditions
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• 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
• Optimality for ill-posed problems under general source conditions
• Geometry of linear ill-posed problems in variable Hilbert scales
• Convergence rates of convex variational regularization
• A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
• Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication 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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