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

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/zamm.19600400908openalex-snapshot
Über die Konvergenz der Iterationsverfahren zur Auflösung linearer Gleichungssysteme im Falle einer singulären Koeffizientenmatrix
inferredcites →https://doi.org/10.1007/bf01395309openalex-snapshot
Solution of underdetermined nonlinear equations by stationary iteration methods
inferredcites →https://doi.org/10.1007/bf01436376openalex-snapshot
Projection method for solving a singular system of linear equations and its applications
inferredcites →https://doi.org/10.1007/bf01436918openalex-snapshot
Characterization of linear stationary iterative processes for solving a singular system of linear equations
inferredcites →https://doi.org/10.1137/0702022openalex-snapshot
On the Solution of Singular and Semidefinite Linear Systems by Iteration

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1002/mma.9931openalex-snapshot
On constrained Kaczmarz algorithm with momentum for image reconstruction
inferred← citeshttps://doi.org/10.1002/nla.2227openalex-snapshot
ChebStaBlkCG: A block variant of ChebFilterCG
inferred← citeshttps://doi.org/10.1002/nla.2591openalex-snapshot
A Semi‐Randomized and Augmented Kaczmarz Method With Simple Random Sampling for Large‐Scale Inconsistent Linear Systems
inferred← citeshttps://doi.org/10.1002/nla.70054openalex-snapshot
Refined Error Bounds for Relaxed Greedy Randomized Kaczmarz Methods
inferred← citeshttps://doi.org/10.1002/num.1690080104openalex-snapshot
Projection methods for the numerical solution of non‐self‐adjoint elliptic partial differential equations
inferred← citeshttps://doi.org/10.1007/978-3-642-30901-4_1openalex-snapshot
Introduction
inferred← citeshttps://doi.org/10.1007/978-3-642-30901-4_2openalex-snapshot
Algorithmic Operators
inferred← citeshttps://doi.org/10.1007/978-3-642-30901-4_3openalex-snapshot
Convergence of Iterative Methods
inferred← citeshttps://doi.org/10.1007/978-3-642-30901-4_4openalex-snapshot
Algorithmic Projection Operators
inferred← citeshttps://doi.org/10.1007/978-3-642-30901-4_5openalex-snapshot
Projection Methods
inferred← citeshttps://doi.org/10.1007/978-94-017-7188-7_10openalex-snapshot
Preconditioners
inferred← citeshttps://doi.org/10.1007/s00211-012-0512-6openalex-snapshot
On the Meany inequality with applications to convergence analysis of several row-action iteration methods
inferred← citeshttps://doi.org/10.1007/s10092-020-00376-4openalex-snapshot
A Note On Convergence Rate of Randomized Kaczmarz Method
inferred← citeshttps://doi.org/10.1007/s10444-026-10301-yopenalex-snapshot
On randomized explicit block Kaczmarz method for solving large linear systems
inferred← citeshttps://doi.org/10.1007/s10543-025-01102-8openalex-snapshot
Deterministic and randomized Kaczmarz methods for $$AXB=C$$ with applications to color image restoration
inferred← citeshttps://doi.org/10.1007/s11075-016-0118-7openalex-snapshot
Single projection Kaczmarz extended algorithms
inferred← citeshttps://doi.org/10.1007/s11075-017-0425-7openalex-snapshot
Convergence rates for Kaczmarz-type algorithms
inferred← citeshttps://doi.org/10.1007/s40314-022-02044-5openalex-snapshot
Multi-step greedy Kaczmarz algorithms with simple random sampling for solving large linear systems
inferred← citeshttps://doi.org/10.1007/s40314-024-02966-2openalex-snapshot
The randomized circumcentered-reflection iteration method for solving consistent linear equations
inferred← citeshttps://doi.org/10.1007/s42967-023-00358-7openalex-snapshot
On Multi-step Greedy Kaczmarz Method for Solving Large Sparse Consistent Linear Systems
inferred← citeshttps://doi.org/10.1007/s42967-024-00447-1openalex-snapshot
A Semi-randomized Block Kaczmarz Method with Simple Random Sampling for Large-Scale Consistent Linear Systems
inferred← citeshttps://doi.org/10.1016/0024-3795(93)00089-iopenalex-snapshot
Block-iterative surrogate projection methods for convex feasibility problems
inferred← citeshttps://doi.org/10.1016/0167-8191(89)90114-2openalex-snapshot
A projection method for solving nonsymmetric linear systems on multiprocessors
inferred← citeshttps://doi.org/10.1016/0168-9274(87)90028-6openalex-snapshot
On some optimization techniques in image reconstruction from projections
inferred← citeshttps://doi.org/10.1016/j.amc.2014.01.098openalex-snapshot
Supplementary projections for the acceleration of Kaczmarz algorithm
inferred← citeshttps://doi.org/10.1016/j.aml.2020.106294openalex-snapshot
A greedy block Kaczmarz algorithm for solving large-scale linear systems
inferred← citeshttps://doi.org/10.1016/j.aml.2022.108290openalex-snapshot
Restarted randomized surrounding methods for solving large linear equations
inferred← citeshttps://doi.org/10.1016/j.apnum.2019.04.008openalex-snapshot
Variant of greedy randomized Kaczmarz for ridge regression
inferred← citeshttps://doi.org/10.1016/j.cam.2021.113828openalex-snapshot
Randomized block Kaczmarz methods with k -means clustering for solving large linear systems
inferred← citeshttps://doi.org/10.1016/j.cam.2026.117478openalex-snapshot
On fast deterministic two-row block Kaczmarz method for solving consistent linear systems
inferred← citeshttps://doi.org/10.1016/s0167-8191(05)80146-2openalex-snapshot
A projection method of the cimmino type for linear algebraic systems
inferred← citeshttps://doi.org/10.1080/00207160.2025.2543153openalex-snapshot
Preprocessed GMRES for fast solution of linear equations
inferred← citeshttps://doi.org/10.1080/00207160108805134openalex-snapshot
Projections and preconditioning for inconsistent least-squares problems
inferred← citeshttps://doi.org/10.1109/83.650854openalex-snapshot
Accelerating the EMML algorithm and related iterative algorithms by rescaled block-iterative methods
inferred← citeshttps://doi.org/10.1137/0913010openalex-snapshot
Row Projection Methods for Large Nonsymmetric Linear Systems
inferred← citeshttps://doi.org/10.1137/1032122openalex-snapshot
The Convergence of Linear Stationary Iterative Processes for Solving Singular Unstructured Systems of Linear Equations
inferred← citeshttps://doi.org/10.1137/120889897openalex-snapshot
Randomized Extended Kaczmarz for Solving Least Squares
inferred← citeshttps://doi.org/10.1137/17m1137747openalex-snapshot
On Greedy Randomized Kaczmarz Method for Solving Large Sparse Linear Systems
inferred← citeshttps://doi.org/10.1137/20m1344937openalex-snapshot
Kaczmarz-Type Inner-Iteration Preconditioned Flexible GMRES Methods for Consistent Linear Systems
inferred← citeshttps://doi.org/10.1137/21m1453475openalex-snapshot
Enhancing Block Cimmino for Sparse Linear Systems with Dense Columns via Schur Complement
inferred← citeshttps://doi.org/10.1137/21m1463306openalex-snapshot
A Deterministic Kaczmarz Algorithm for Solving Linear Systems
inferred← citeshttps://doi.org/10.1137/s0036144593251710openalex-snapshot
On Projection Algorithms for Solving Convex Feasibility Problems
inferred← citeshttps://doi.org/10.1155/2020/7464212openalex-snapshot
On Randomized Sampling Kaczmarz Method with Application in Compressed Sensing
inferred← citeshttps://doi.org/10.14708/wm.v46i1.138openalex-snapshot
O algorytmie Kaczmarza
inferred← citeshttps://doi.org/10.21203/rs.3.rs-4417069/v1openalex-snapshot
On maximum residual block Kaczmarz method for solving large consistent linear systems
inferred← citeshttps://doi.org/10.2478/auom-2018-0015openalex-snapshot
On Remotest set and Random controls in Kaczmarz algorithm
inferred← citeshttps://doi.org/10.3390/axioms15070491openalex-snapshot
Block Subgradient Greedy Kaczmarz Methods for Robotic Grasping Problems
inferred← citeshttps://doi.org/10.3934/math.20241614openalex-snapshot
On maximum residual block Kaczmarz method for solving large consistent linear systems
inferred← citeshttps://doi.org/10.4208/eajam.300921.170422openalex-snapshot
A Partially Greedy Randomized Extended Gauss-Seidel Method for Solving Large Linear Systems
inferred← citeshttps://doi.org/10.4208/nmtma.oa-2018-0039openalex-snapshot
A New Theoretical Estimate for the Convergence Rate of the Maximal Weighted Residual Kaczmarz Algorithm
inferred← citeshttps://doi.org/10.48550/arxiv.1504.00231openalex-snapshot
Single Projection Kaczmarz Extended Algorithms
inferred← citeshttps://doi.org/10.48550/arxiv.1701.08002openalex-snapshot
Convergence rates for Kaczmarz-type algorithms
inferred← citeshttps://doi.org/10.48550/arxiv.1702.02729openalex-snapshot
A note on Kaczmarz algorithm with remotest set control sequence
inferred← citeshttps://doi.org/10.48550/arxiv.2011.14693openalex-snapshot
A Kaczmarz Method with Simple Random Sampling for Solving Large Linear Systems
inferred← citeshttps://doi.org/10.48550/arxiv.2106.13368openalex-snapshot
On Kaczmarz method with oblique projection for solving large overdetermined linear systems
inferred← citeshttps://doi.org/10.48550/arxiv.2108.09173openalex-snapshot
Straggler-Robust Distributed Optimization in Parameter-Server Networks
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