Connections between the Cimmino-method and the Kaczmarz-method for the solution of singular and regular systems of equations

DOI10.1007/BF02242280zbMath0537.65027OpenAlexW304534868MaRDI QIDQ792735

Rainer Ansorge

Publication date: 1985

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02242280

zbMATH Keywords

fast convergenceCimmino-methodKaczmarz-methodnon-regular coefficient matrices

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (18)

A Deterministic Kaczmarz Algorithm for Solving Linear Systems ⋮ Enhancing Block Cimmino for Sparse Linear Systems with Dense Columns via Schur Complement ⋮ Block-iterative surrogate projection methods for convex feasibility problems ⋮ Single projection Kaczmarz extended algorithms ⋮ On some optimization techniques in image reconstruction from projections ⋮ Restarted randomized surrounding methods for solving large linear equations ⋮ A greedy block Kaczmarz algorithm for solving large-scale linear systems ⋮ Randomized block Kaczmarz methods with \(k\)-means clustering for solving large linear systems ⋮ Convergence rates for Kaczmarz-type algorithms ⋮ A note on convergence rate of randomized Kaczmarz method ⋮ On Greedy Randomized Kaczmarz Method for Solving Large Sparse Linear Systems ⋮ On the Meany inequality with applications to convergence analysis of several row-action iteration methods ⋮ Kaczmarz-Type Inner-Iteration Preconditioned Flexible GMRES Methods for Consistent Linear Systems ⋮ Projections and preconditioning for inconsistent least-squares problems ⋮ Variant of greedy randomized Kaczmarz for ridge regression ⋮ Kaczmarz-Type Inner-Iteration Preconditioned Flexible GMRES Methods for Consistent Linear Systems ⋮ Multi-step greedy Kaczmarz algorithms with simple random sampling for solving large linear systems ⋮ A Partially Greedy Randomized Extended Gauss-Seidel Method for Solving Large Linear Systems

Cites Work

• Characterization of linear stationary iterative processes for solving a singular system of linear equations
• Projection method for solving a singular system of linear equations and its applications
• Über die Konvergenz der Iterationsverfahren zur Auflösung linearer Gleichungssysteme im Falle einer singulären Koeffizientenmatrix
• On the Solution of Singular and Semidefinite Linear Systems by Iteration
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