A mixed Newton-Tikhonov method for nonlinear ill-posed problems

DOI10.1007/s10483-009-0608-2zbMath1178.65059OpenAlexW1998981572MaRDI QIDQ735296

Guo-qiang He, Chuan-Gang Kang

Publication date: 21 October 2009

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-009-0608-2

zbMATH Keywords

algorithmstabilityconvergencenumerical experimentsHilbert spacesnonlinear operator equationregularization methodnonlinear ill-posed problemsinverse heat conduction problemmixed Newton-Tikhonov methodnonlinear Fréchet differentiable mapping

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30) 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)

Uses Software

• NewtonLib

Cites Work

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• Iterative regularization methods for nonlinear ill-posed problems
• A Newton type iterative method for heat-conduction inverse problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems
• A convergence analysis of the iteratively regularized Gauss–Newton method under the Lipschitz condition
• A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions
• On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems

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