Convergence rates of the Kaczmarz-Tanabe method for linear systems

DOI10.1016/j.cam.2021.113577zbMath1472.65039OpenAlexW3148577423MaRDI QIDQ2029445

Chuan-Gang Kang

Publication date: 3 June 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113577

zbMATH Keywords

convergence ratessingular value decompositionKaczmarz-Tanabe method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08)

Related Items (4)

Greedy randomized and maximal weighted residual Kaczmarz methods with oblique projection ⋮ A class of residual-based extended Kaczmarz methods for solving inconsistent linear systems ⋮ The standard forms and convergence theory of the Kaczmarz-Tanabe type methods for solving linear systems ⋮ Gauss-Seidel method with oblique direction

Uses Software

• AIR tools

Cites Work

• Unnamed Item
• Unnamed Item
• A randomized Kaczmarz algorithm with exponential convergence
• A projection method for solving nonsymmetric linear systems on multiprocessors
• Generalized inverses. Theory and applications.
• The extensions of convergence rates of Kaczmarz-type methods
• The dual Kaczmarz algorithm
• Convergence rates for Kaczmarz-type algorithms
• AIR tools II: algebraic iterative reconstruction methods, improved implementation
• Paved with good intentions: analysis of a randomized block Kaczmarz method
• Projection method for solving a singular system of linear equations and its applications
• Projection methods: an annotated bibliography of books and reviews
• Solving systems of phaseless equations via Kaczmarz methods: a proof of concept study
• Preasymptotic convergence of randomized Kaczmarz method

This page was built for publication: Convergence rates of the Kaczmarz-Tanabe method for linear systems