On the quasioptimal regularization parameter choices for solving ill-posed problems

DOI10.1515/JIIP.2007.023zbMath1136.65053OpenAlexW1972530969MaRDI QIDQ5421232

Toomas Raus, Uno Hämarik

Publication date: 22 October 2007

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

Full work available at URL: https://doi.org/10.1515/jiip.2007.023

zbMATH Keywords

discrepancy principlelinear ill-posed problemsregularization methodsregularization parameterLepskii principlemonotone error rule.quasioptimal choice

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (11)

Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function ⋮ Converse Results, Saturation and Quasi-optimality for Lavrentiev Regularization of Accretive Problems ⋮ Characterizations of Variational Source Conditions, Converse Results, and Maxisets of Spectral Regularization Methods ⋮ On the quasi-optimal rules for the choice of the regularization parameter in case of a noisy operator ⋮ A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level ⋮ Comparing parameter choice methods for regularization of ill-posed problems ⋮ A simplified L-curve method as error estimator ⋮ On Minimization Strategies for Choice of the Regularization Parameter in Ill-Posed Problems ⋮ About the Balancing Principle for Choice of the Regularization Parameter ⋮ Monotonicity of error of regularized solution and its use for parameter choice ⋮ Parameter Choices for Fast Harmonic Spline Approximation

Cites Work

• Regularization in Hilbert scales under general smoothing conditions
• A Lepskij-type stopping rule for regularized Newton methods
• Regularization without preliminary knowledge of smoothness and error behaviour
• Discretization strategy for linear ill-posed problems in variable Hilbert scales
• The use of monotonicity for choosing the regularization parameter in ill-posed problems
• On the Adaptive Selection of the Parameter in Regularization of Ill-Posed Problems
• Convergence rates for Tikhonov regularization from different kinds of smoothness conditions

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