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Modulus of continuity and conditional stability for linear regularization schemes
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M. Schieck
Published/Copyright:
February 4, 2009
Abstract
This paper surveys the concept of conditional stability for linear ill-posed problems with error estimates based on the modulus of continuity. Combining the ideas of [Hofmann, Mathé, Schieck, J. Inv. Ill-Posed Problems 16: 569–587, 2008] and [Kabanikhin, Schieck, J. Inv. Ill-Posed Problems 16: 267–282, 2008] fundamental properties are formulated and convergence rates results for regularized solutions concerning linear regularization schemes are carried out.
Key words.: Linear ill-posed problems; modulus of continuity; conditional stability; general regularization methods; profile functions
Received: 2008-07-25
Published Online: 2009-02-04
Published in Print: 2009-February
© de Gruyter 2009
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Keywords for this article
Linear ill-posed problems;
modulus of continuity;
conditional stability;
general regularization methods;
profile functions
Articles in the same Issue
- Minisymposium — Recent progress in regularization theory
- Recent results on the quasi-optimality principle
- An iterative thresholding-like algorithm for inverse problems with sparsity constraints in Banach space
- Regularization in Banach spaces — convergence rates by approximative source conditions
- On a parameter identification problem in linear elasticity
- Modified Landweber iterations in a multilevel algorithm applied to inverse problems in piezoelectricity
- On the role of sparsity in inverse problems
- Optimal convergence rates for Tikhonov regularization in Besov scales
- An overview on convergence rates for Tikhonov regularization methods for non-linear operators
- Modulus of continuity and conditional stability for linear regularization schemes
- Acceleration of the generalized Landweber method in Banach spaces via sequential subspace optimization
