Convergence analysis of an inexact iteratively regularized Gauss-Newton method under general source conditions

DOI10.1515/jiip.2007.017zbMath1129.65043OpenAlexW1967275446MaRDI QIDQ5427274

Stefan Langer, Thorsten Hohage

Publication date: 19 November 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.2007.017

zbMATH Keywords

Hilbert spacesTikhonov regularizationdiscrepancy principlesource conditionsnonlinear inverse problemsGauss-Newton methodnonlinear ill-posed operator equationregularized Newton methodsconvergenge rates

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) Numerical solution to inverse problems in abstract spaces (65J22)

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Cites Work

• A posteriori parameter choice strategies for some Newton type methods for the regularization of nonlinear ill-posed problems
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• On the numerical solution of a three-dimensional inverse medium scattering problem
• A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
• On the regularization of nonlinear ill-posed problems via inexact Newton iterations
• Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
• On convergence rates for the iteratively regularized Gauss-newton method
• Some Newton-type methods for the regularization of nonlinear ill-posed problems
• Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem
• Regularizing properties of a truncated newton-cg algorithm for nonlinear inverse problems
• Geometry of linear ill-posed problems in variable Hilbert scales
• Inexact Newton Regularization Using Conjugate Gradients as Inner Iteration

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