Impact of conditional stability: Convergence rates for general linear regularization methods
From MaRDI portal
Publication:3516772
DOI10.1515/JIIP.2008.016zbMath1143.47061MaRDI QIDQ3516772
Matthias Schieck, Sergey I. Kabanikhin
Publication date: 11 August 2008
Published in: Journal of Inverse and Ill-posed Problems (Search for Journal in Brave)
convergence ratesconditional stabilitylinear ill-posed problemsource conditionprofile functiongeneral linear regularization methods
Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Applications of operator theory in numerical analysis (47N40)
Related Items
Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities, A modified method for a Cauchy problem of the Helmholtz equation, Regularization methods for a problem of analytic continuation, An Inverse Diffraction Problem: Shape Reconstruction, Definitions and examples of inverse and ill-posed problems, Modulus of continuity for conditionally stable ill-posed problems in Hilbert space, Solving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularization, Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation, Modulus of continuity and conditional stability for linear regularization schemes, Conditional Stability Estimates and Regularization with Applications to Cauchy Problems for the Helmholtz Equation
Cites Work
- Regularization in Hilbert scales under general smoothing conditions
- Interpolation in variable Hilbert scales with application to inverse problems
- Using a priori information about a solution of an ill-posed problem for constructing regularizing algorithms and their applications
- Conditional stability stopping rule for gradient methods applied to inverse and ill-posed problems
- Analysis of Profile Functions for General Linear Regularization Methods
- Geometry of linear ill-posed problems in variable Hilbert scales
- On Lavrentiev Regularization for Ill-Posed Problems in 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
- Regularization of exponentially ill-posed problems
- Saturation of Regularization Methods for Linear Ill-Posed Problems in Hilbert Spaces
- Variable hilbert scales and their interpolation inequalities with applications to tikhonov regularization
- Convergence rate estimation of gradient methodsviaconditional stability of inverse and ill-posed problems
- 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
- Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
