Further convergence results on the general iteratively regularized Gauss-Newton methods under the discrepancy principle

DOI10.1090/S0025-5718-2012-02665-2zbMath1277.65041OpenAlexW1997341639MaRDI QIDQ2840626

Qi-nian Jin

Publication date: 23 July 2013

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-2012-02665-2

zbMATH Keywords

convergencediscrepancy principlenonlinear inverse problemsorder optimalitygeneral iteratively regularized Gauss-Newton methods

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)

Related Items (7)

Improving epidemic size prediction through stable reconstruction of disease parameters by reduced iteratively regularized Gauss-Newton algorithm ⋮ A Discretizing Levenberg-Marquardt Scheme for Solving Nonlinear Ill-Posed Integral Equations ⋮ Simplified generalized Gauss-Newton method for nonlinear ill-posed operator equations in Hilbert scales ⋮ Iterative Lavrentiev regularization method under a heuristic rule for nonlinear ill-posed operator equations ⋮ Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems ⋮ Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule ⋮ On application of asymptotic generalized discrepancy principle to the analysis of epidemiology models

Cites Work

• Inexact Newton regularization methods in Hilbert scales
• On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems
• The problem of the convergence of the iteratively regularized Gauss- Newton method
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• On convergence rates for the iteratively regularized Gauss-newton method
• Some Newton-type methods for the regularization of nonlinear ill-posed problems
• Convergence rates for Tikhonov regularization from different kinds of smoothness conditions
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