Convergence rates for an iteratively regularized Newton–Landweber iteration in Banach space

DOI10.1088/0266-5611/29/2/025010zbMath1285.65033arXiv1408.5026OpenAlexW2042052314MaRDI QIDQ4917603

Barbara Kaltenbacher, Ivan Tomba

Publication date: 2 May 2013

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.5026

zbMATH Keywords

duality mappingBanach spaceconvergence ratenonlinear ill-posed problemdiscrepancy principleregularization methodstopping ruleLandweber iterationBregman distancevariational source conditionGauss--Newton iteration

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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REGINN-IT method with general convex penalty terms for nonlinear inverse problems ⋮ Convergence analysis of inexact Newton–Landweber iteration under Hölder stability ⋮ Error estimates for the iteratively regularized Newton-Landweber method in Banach spaces under approximate source conditions ⋮ Simplified Levenberg–Marquardt method in Banach spaces for nonlinear ill-posed operator equations ⋮ Heuristic rule for inexact Newton-Landweber iteration with convex penalty terms of nonlinear: ill-posed problems ⋮ Iterative Solution Methods ⋮ Accelerated Iterative Regularization via Dual Diagonal Descent ⋮ Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space

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