A convergence analysis of regularization by discretization in preimage space

DOI10.1090/S0025-5718-2012-02596-8zbMath1281.65087MaRDI QIDQ2840002

Jonas Offtermatt, Barbara Kaltenbacher

Publication date: 17 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

discretizationconvergenceregularizationinverse problemsHilbert spacesdiscrepancy principleill-posed operator equationsleast-squares projection

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with linear operators (65J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items

Projected Tikhonov regularization method for Fredholm integral equations of the first kind, Adaptive Spectral Inversion for inverse medium problems, Least-Squares Collocation for Higher-Index DAEs: Global Approach and Attempts Toward a Time-Stepping Version, Least-squares collocation for higher-index linear differential-algebraic equations: Estimating the instability threshold, Adaptive spectral decompositions for inverse medium problems, Least-squares collocation for linear higher-index differential-algebraic equations, A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations, ON THE SELF-REGULARIZATION OF ILL-POSED PROBLEMS BY THE LEAST ERROR PROJECTION METHOD, On the sensitivity of implementations of a least-squares collocation method for linear higher-index differential-algebraic equations

Cites Work

• Iterative regularization methods for nonlinear ill-posed problems
• Convergence rates of a multilevel method for the regularization of nonlinear ill-posed problems
• Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
• Nonconvergence results for the application of least-squares estimation to ill-posed problems
• Linear integral equations.
• Statistical and computational inverse problems.
• A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Ill-posed problems with a priori information
• Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems
• A refinement and coarsening indicator algorithm for finding sparse solutions of inverse problems
• On the regularizing properties of a full multigrid method for ill-posed problems
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• V-cycle convergence of some multigrid methods for ill-posed problems
• Regularization by projection with a posteriori discretization level choice for linear and nonlinear ill-posed problems
• Refinement and coarsening indicators for adaptive parametrization: application to the estimation of hydraulic transmissivities
• Regularization by projection: Approximation theoretic aspects and distance functions
• Regularization by projection in variable Hilbert scales
• Toward Global Convergence for Strongly Nonlinear Ill-Posed Problems via a Regularizing Multilevel Approach
• An introduction to the mathematical theory of inverse problems
• On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item