A convergence analysis of the iteratively regularized Gauss–Newton method under the Lipschitz condition

DOI10.1088/0266-5611/24/4/045002zbMath1153.65058arXiv0803.2373OpenAlexW3105678951MaRDI QIDQ3521047

Qi-nian Jin

Publication date: 27 August 2008

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

Full work available at URL: https://arxiv.org/abs/0803.2373

zbMATH Keywords

Hilbert spaceparameter identificationnonlinear operator equationregularization methodGauss-Newton methodnonlinear ill-posed inverse problemsPoisson-equation

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical solution to inverse problems in abstract spaces (65J22)

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On a class of frozen regularized Gauss-Newton methods for nonlinear inverse problems ⋮ Parameter estimation with the multigrid-homotopy method for a nonlinear diffusion equation ⋮ A Convergence Analysis of the Iterated Lavrentiev Regularization Method under a Lipschitz Condition ⋮ Convergence analysis of a proximal Gauss-Newton method ⋮ Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems ⋮ A convergence analysis of nonlinear implicit iterative method for nonlinear ill-posed problems ⋮ Inverse problem of groundwater modeling by iteratively regularized Gauss-Newton method with a nonlinear regularization term ⋮ Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule ⋮ A Regularized Newton-Like Method for Nonlinear PDE ⋮ A mixed Newton-Tikhonov method for nonlinear ill-posed problems ⋮ On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems ⋮ Nonlinear implicit iterative method for solving nonlinear ill-posed problems ⋮ Theoretical and Numerical Study of Iteratively Truncated Newton’s Algorithm

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