On Kaczmarz's projection iteration as a direct solver for linear least squares problems

DOI10.1016/j.laa.2011.02.017zbMath1238.65031OpenAlexW2043324428MaRDI QIDQ651214

Constantin Popa, Harald Köstler, Ulrich Rüde, Tobias Preclik

Publication date: 8 December 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.02.017

zbMATH Keywords

stabilitynumerical examplesMoore-Penrose inversesKaczmarz algorithmdirect projection methodsextended Kaczmarz algorithmlinear least squares problemsrigid multibody dynamicsround-off analysis

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Iterative numerical methods for linear systems (65F10) Dynamics of multibody systems (70E55)

Related Items (10)

Greedy randomized and maximal weighted residual Kaczmarz methods with oblique projection ⋮ Convergence Properties of the Randomized Extended Gauss--Seidel and Kaczmarz Methods ⋮ Supplementary projections for the acceleration of Kaczmarz algorithm ⋮ Adaptively sketched Bregman projection methods for linear systems ⋮ A Sampling Kaczmarz--Motzkin Algorithm for Linear Feasibility ⋮ Rows versus Columns: Randomized Kaczmarz or Gauss--Seidel for Ridge Regression ⋮ Randomized block Kaczmarz method with projection for solving least squares ⋮ Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm ⋮ Gauss-Seidel method with oblique direction ⋮ Greed Works: An Improved Analysis of Sampling Kaczmarz--Motzkin

Cites Work

• Projection methods for linear systems
• Block-iterative methods for consistent and inconsistent linear equations
• A class of direct methods for linear systems
• Extensions of block-projections methods with relaxation parameters to inconsistent and rank-deficient least-squares problems
• Projection method for solving a singular system of linear equations and its applications
• A Direct Projection Method for Sparse Linear Systems
• A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
• The Vector Method of Solving Simultaneous Linear Equations
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