A Note on the Nonlinear Landweber Iteration

DOI10.1080/01630563.2014.884586zbMath1307.65078OpenAlexW2035661022MaRDI QIDQ2929514

Martin Hanke

Publication date: 12 November 2014

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2014.884586

zbMATH Keywords

Hilbert spacediscrepancy principleregularization methodnonlinear ill-posed problemsLandweber iterationoperator equationmonotonicity rule

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 (4)

A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods ⋮ A reduced basis Landweber method for the identification of piecewise constant Robin coefficient in an elliptic equation ⋮ A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration ⋮ A New Gradient Method for Ill-Posed Problems

Cites Work

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• Iterative regularization methods for nonlinear ill-posed problems
• A uniform approach to gradient methods for linear operator equations
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• The use of monotonicity for choosing the regularization parameter in ill-posed problems

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