Regularization by projection: Approximation theoretic aspects and distance functions

DOI10.1515/jiip.2007.029zbMath1134.65039OpenAlexW2065759858MaRDI QIDQ5432658

Peter Mathé, Bernd Hofmann, Sergei V. Pereverzyev

Publication date: 17 December 2007

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2007.029

zbMATH Keywords

convergence rateserror estimatesnumerical examplesfixed-point iterationnonlinear ill-posed problemsdistance functionsbalancing principlerange inclusionsJackson- and Bernstein type inequalitiesregulation by discretization

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items

Designing truncated priors for direct and inverse Bayesian problems, Lavrentiev's regularization method in Hilbert spaces revisited, On Self-regularization of Ill-Posed Problems in Banach Spaces by Projection Methods, Adaptive Spectral Inversion for inverse medium problems, Regularization Methods for Ill-Posed Problems, Regularization by projection in variable Hilbert scales, A convergence analysis of regularization by discretization in preimage space, ON THE SELF-REGULARIZATION OF ILL-POSED PROBLEMS BY THE LEAST ERROR PROJECTION METHOD, Optimal indirect estimation for linear inverse problems with discretely sampled functional data, DISCREPANCY SETS FOR COMBINED LEAST SQUARES PROJECTION AND TIKHONOV REGULARIZATION

Cites Work

• Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Newton–Tikhonov regularization of ill-posed Hammerstein operator equation
• Analysis of Profile Functions for General Linear Regularization Methods
• A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
• Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
• Factors influencing the ill-posedness of nonlinear problems
• Geometry of linear ill-posed problems in variable Hilbert scales
• Discretization strategy for linear ill-posed problems in variable Hilbert scales
• Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
• On Weakly Nonlinear Inverse Problems
• Convergence rates for Tikhonov regularization based on range inclusions
• Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
• The Lepskii principle revisited
• Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions