Regularization of linear ill-posed problems with noisy right hand side and noisy operator

DOI10.1515/JIIP.2008.027zbMath1153.65054OpenAlexW2061702245MaRDI QIDQ3529876

Ulrich Tautenhahn

Publication date: 14 October 2008

Published in: JIIP (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2008.027

zbMATH Keywords

inverse problemsHilbert spacesTikhonov regularizationlinear operator equationill-posed problemsinverse heat conduction problemregularized total least squaresgeneral source conditionsnoisy operatornoisy right hand sideorder optimal error bounds

Mathematics Subject Classification ID

Heat equation (35K05) Inverse problems for PDEs (35R30) Numerical solutions to equations with linear operators (65J10) 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 (8)

Semi-heuristic parameter choice rules for Tikhonov regularisation with operator perturbations ⋮ Exponential Inequalities in Stochastic Inverse Problems Using an Iterative Method ⋮ On the generalized discrepancy principle for Tikhonov regularization in Hilbert scales ⋮ Regularized Linear Inversion with Randomized Singular Value Decomposition ⋮ Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers ⋮ A survey on variational characterizations for nonlinear eigenvalue problems ⋮ Solving inverse problems using data-driven models ⋮ Simple and efficient determination of the Tikhonov regularization parameter chosen by the generalized discrepancy principle for discrete ill-posed problems

Cites Work

• On a quadratic eigenproblem occurring in regularized total least squares
• Regularized total least squares based on quadratic eigenvalue problem solvers
• Regularization in Hilbert scales under general smoothing conditions
• Finding a Global Optimal Solution for a Quadratically Constrained Fractional Quadratic Problem with Applications to the Regularized Total Least Squares
• Geometry of linear ill-posed problems in variable Hilbert scales
• Regularization of exponentially ill-posed problems
• Efficient Algorithms for Solution of Regularized Total Least Squares
• Tikhonov Regularization and Total Least Squares
• Variable hilbert scales and their interpolation inequalities with applications to tikhonov regularization
• On the Solution of the Tikhonov Regularization of the Total Least Squares Problem
• SCALES OF BANACH SPACES

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