A New Gradient Method for Ill-Posed Problems

DOI10.1080/01630563.2017.1414061zbMath1486.65056OpenAlexW2775344568MaRDI QIDQ4639213

Andreas Neubauer

Publication date: 3 May 2018

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

Full work available at URL: https://doi.org/10.1080/01630563.2017.1414061

zbMATH Keywords

gradient methodsdiscrepancy principlestopping ruleLandweber iterationsteepest descent methodminimal error methodlinear and nonlinear ill-posed problems

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (7)

A Modified Minimal Error Method for Solving Nonlinear Integral Equations via Multiscale Galerkin Methods ⋮ A Discretizing Levenberg-Marquardt Scheme for Solving Nonlinear Ill-Posed Integral Equations ⋮ A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration ⋮ Analysis of the Block Coordinate Descent Method for Linear Ill-Posed Problems ⋮ A note on the minimization of a Tikhonov functional with ℓ¹-penalty ⋮ Optimal convergence rates for inexact Newton regularization with CG as inner iteration ⋮ A mathematical framework for nonlinear wavefront reconstruction in adaptive optics systems with Fourier-type wavefront sensing

Cites Work

• Some generalizations for Landweber iteration for nonlinear ill-posed problems in Hilbert scales
• The instability of some gradient methods for ill-posed problems
• Iterative regularization methods for nonlinear ill-posed problems
• Convergence rate results for steepest descent type method for nonlinear ill-posed equations
• A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• On Landweber iteration for nonlinear ill-posed problems in Hilbert scales
• An analysis of a multi-level projected steepest descent iteration for nonlinear inverse problems in Banach spaces subject to stability constraints
• On projective Landweber–Kaczmarz methods for solving systems of nonlinear ill-posed equations
• A Note on the Nonlinear Landweber Iteration
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