Inexact Newton regularization methods in Hilbert scales

DOI10.1007/s00211-010-0342-3zbMath1214.65030arXiv1009.3868OpenAlexW1970209646MaRDI QIDQ629902

Ulrich Tautenhahn, Qi-nian Jin

Publication date: 10 March 2011

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.3868

zbMATH Keywords

numerical examplesnonlinear operator equationdiscrepancy principleregularization methodsinexact Newton methodHilbert scalesfractional powers of positive definite operatorsnonlinear Fréchet differentiable operatorspectral filter function

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (7)

Error estimates for the iteratively regularized Newton-Landweber method in Banach spaces under approximate source conditions ⋮ A convergence analysis of an inexact Newton-Landweber iteration method for nonlinear problem ⋮ On the order optimality of the regularization via inexact Newton iterations ⋮ A two step Newton type iteration for ill-posed Hammerstein type operator equations in Hilbert scales ⋮ Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales ⋮ Accuracy estimation for a class of iteratively regularized Gauss-Newton methods with a posteriori stopping rule ⋮ Further convergence results on the general iteratively regularized Gauss-Newton methods under the discrepancy principle

Cites Work

• Unnamed Item
• The regularizing Levenberg-Marquardt scheme is of optimal order
• Towards a general convergence theory for inexact Newton regularizations
• On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• On Landweber iteration for nonlinear ill-posed problems in Hilbert scales
• A regularizing Levenberg - Marquardt scheme, with applications to inverse groundwater filtration problems
• Inexact Newton Methods
• On a general regularization scheme for nonlinear ill-posed problems: II. Regularization in Hilbert scales
• On the regularization of nonlinear ill-posed problems via inexact Newton iterations
• The analysis of a discrete scheme of the iteratively regularized Gauss-Newton method
• Error bounds for regularized solutions of nonlinear ill-posed problems
• A convergence analysis of the exponential Euler iteration for nonlinear ill-posed problems
• Error Estimates for Regularization Methods in Hilbert Scales
• On convergence rates of inexact Newton regularizations

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