Convergence analysis of a block iterative version of the loping Landweber-Kaczmarz iteration

DOI10.1016/j.na.2009.07.016zbMath1239.65023OpenAlexW1987059360MaRDI QIDQ425920

Markus Haltmeier

Publication date: 9 June 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.07.016

zbMATH Keywords

regularizationintegral equationsLandweber iterationblock iterative methodsill-posed equationsKaczmarz iteration

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (9)

Analysis of the Block Coordinate Descent Method for Linear Ill-Posed Problems ⋮ Iterative methods for photoacoustic tomography in attenuating acoustic media ⋮ Convergence rates for Kaczmarz-type regularization methods ⋮ Column-oriented algebraic iterative methods for nonnegative constrained least squares problems ⋮ Error minimizing relaxation strategies in Landweber and Kaczmarz type iterations ⋮ Convergence analysis for column-action methods in image reconstruction ⋮ Weak, Strong, and Linear Convergence of a Double-Layer Fixed Point Algorithm ⋮ Analysis of a generalized regularized Gauss–Newton method under heuristic rule in Banach spaces ⋮ Convergence and Semi-Convergence of a Class of Constrained Block Iterative Methods

Cites Work

• Block-iterative methods for consistent and inconsistent linear equations
• On steepest-descent-Kaczmarz methods for regularizing systems of nonlinear ill-posed equations
• Variational methods in imaging
• Iterative algorithms for large partitioned linear systems, with applications to image reconstruction
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Kaczmarz methods for regularizing nonlinear ill-posed equations. II: Applications
• Kaczmarz methods for regularizing nonlinear ill-posed equations. I: Convergence analysis
• Mathematical Methods in Image Reconstruction
• On Projection Algorithms for Solving Convex Feasibility Problems
• On regularization methods of EM-Kaczmarz type
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