Range Inclusions and Approximate Source Conditions with General Benchmark Functions

DOI10.1080/01630560701749649zbMath1136.47008OpenAlexW2024237376MaRDI QIDQ5438280

Dana Düvelmeyer, Bernd Hofmann, Masahiro Yamamoto

Publication date: 23 January 2008

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630560701749649

zbMATH Keywords

convergence ratesTikhonov regularizationlinear ill-posed problemsHölder exponentdistance functionsource conditionindex functionrange inclusionqualification

Mathematics Subject Classification ID

Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

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Cites Work

• Unnamed Item
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• Regularization in Hilbert scales under general smoothing conditions
• Interpolation in variable Hilbert scales with application to inverse problems
• Regularization of some linear ill-posed problems with discretized random noisy data
• Analysis of Profile Functions for General Linear Regularization Methods
• Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
• On Converse and Saturation Results for Tikhonov Regularization of Linear Ill-Posed Problems
• Optimality for ill-posed problems under general source conditions
• Geometry of linear ill-posed problems in variable Hilbert scales
• Discretization strategy for linear ill-posed problems in variable Hilbert scales
• One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
• Saturation of Regularization Methods for Linear Ill-Posed Problems in Hilbert Spaces
• Functional Analysis
• Variable hilbert scales and their interpolation inequalities with applications to tikhonov regularization
• On the analysis of distance functions for linear ill-posed problems with an application to the integration operator inL²
• Convergence rates for Tikhonov regularization based on range inclusions
• Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators
• Convergence rates for Tikhonov regularization from different kinds of smoothness conditions