Block-iterative methods for consistent and inconsistent linear equations
From MaRDI portal
Publication:754606
DOI10.1007/BF01396365zbMath0416.65031MaRDI QIDQ754606
Publication date: 1980
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/186304
generalized solutiongeneralized inversesmatrixleast squares solutioniterative schemesminimum norm solutionlinear system of equationsoptimal values of the iteration parameters
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Iterative numerical methods for linear systems (65F10)
Related Items
A general extending and constraining procedure for linear iterative methods, Convergence of a randomized Douglas-Rachford method for linear system, Solving systems of nonlinear equations by means of an accelerated successive orthogonal projections method, A projection method for semidefinite linear systems and its applications, A multiprojection algorithm using Bregman projections in a product space, Constraining by a family of strictly nonexpansive idempotent functions with applications in image reconstruction, Block row projection method based on M-matrix splitting, Convergence Properties of the Randomized Extended Gauss--Seidel and Kaczmarz Methods, On greedy randomized average block Kaczmarz method for solving large linear systems, On block accelerations of quantile randomized Kaczmarz for corrupted systems of linear equations, Insoluble multicriteria linear programming problems, Solving systems of phaseless equations via Kaczmarz methods: a proof of concept study, Comments on ``Symmetric successive overrelaxation methods for rank deficient linear systems, Quantile-Based Iterative Methods for Corrupted Systems of Linear Equations, Parallel application of block-iterative methods in medical imaging and radiation therapy, Restarted randomized surrounding methods for solving large linear equations, A Novel Partitioning Method for Accelerating the Block Cimmino Algorithm, A parallel projection method for solving generalized linear least-squares problems, A Robust Algebraic Domain Decomposition Preconditioner for Sparse Normal Equations, Iterative solution of simultaneous equations, On greedy randomized block Kaczmarz method for consistent linear systems, On randomized partial block Kaczmarz method for solving huge linear algebraic systems, Inhomogeneous turbulent field diagnostics by distance-dependent tomographic reconstruction techniques, Randomized Kaczmarz with averaging, A greedy block Kaczmarz algorithm for solving large-scale linear systems, Extensions of block-projections methods with relaxation parameters to inconsistent and rank-deficient least-squares problems, A unified treatment of some perturbed fixed point iterative methods with an infinite pool of operators, Block Kaczmarz method with inequalities, An almost-maximal residual tensor block Kaczmarz method for large tensor linear systems, On adaptive block coordinate descent methods for ridge regression, Row Replicated Block Cimmino, The standard forms and convergence theory of the Kaczmarz-Tanabe type methods for solving linear systems, Faster Deterministic Pseudoinverse-Free Block Extension of Motzkin Method for Large Consistent Linear Systems, An LP-based algorithm for the correction of inconsistent linear equation and inequality systems, On pseudoinverse-free block maximum residual nonlinear Kaczmarz method for solving large-scale nonlinear system of equations, Convergence analysis of a block iterative version of the loping Landweber-Kaczmarz iteration, On some methods for entropy maximization and matrix scaling, Iterative algorithms for large partitioned linear systems, with applications to image reconstruction, On fast greedy block Kaczmarz methods for solving large consistent linear systems, Paved with good intentions: analysis of a randomized block Kaczmarz method, A Sampling Kaczmarz--Motzkin Algorithm for Linear Feasibility, Rows versus Columns: Randomized Kaczmarz or Gauss--Seidel for Ridge Regression, Strong underrelaxation in Kaczmarz's method for inconsistent systems, On Kaczmarz's projection iteration as a direct solver for linear least squares problems, On block Gaussian sketching for the Kaczmarz method, Solution of underdetermined nonlinear equations by stationary iteration methods, Column-oriented algebraic iterative methods for nonnegative constrained least squares problems, Choosing the relaxation parameter in sequential block-iterativemethods for linear systems, Randomized Extended Average Block Kaczmarz for Solving Least Squares, Randomized block Kaczmarz method with projection for solving least squares, Convergence studies on block iterative algorithms for image reconstruction, A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography, Perturbation‐resilient block‐iterative projection methods with application to image reconstruction from projections, Convergence analysis for column-action methods in image reconstruction, Partitioning strategies for the block Cimmino algorithm, Successive overrelaxation methods for solving the rank deficient linear least squares problem, CARP-CG: A robust and efficient parallel solver for linear systems, applied to strongly convection dominated PDEs, A refinement of an iterative orthogonal projection method, Stochastic gradient descent, weighted sampling, and the randomized Kaczmarz algorithm, Randomized subspace actions and fusion frames, Faster Randomized Block Kaczmarz Algorithms, On the error estimate of the randomized double block Kaczmarz method, On maximum residual block and two-step Gauss-Seidel algorithms for linear least-squares problems, Generalized row-action methods for tomographic imaging, Unnamed Item, A stationary iterative pseudoinverse algorithm, A projection method for least-squares solutions to overdetermined systems of linear inequalities, Convergence of string-averaging method for a class of operators, Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, Successive over-relaxation methods in the analysis of variance, Parallelization of Hermitian positive definite systems of equations: a hierarchical Jacobi approach, Sampled limited memory methods for massive linear inverse problems, Symmetric successive overrelaxation methods for solving the rank deficient linear least squares problem, The Augmented Block Cimmino Distributed Method, Extensions of the Augmented Block Cimmino Method to the Solution of Full Rank Rectangular Systems, The best approximate solution of the inconsistent linear system via a quadratic penalty function, Convergence results for an accelerated nonlinear Cimmino algorithm, Convergence analysis for Kaczmarz-type methods in a Hilbert space framework, Randomized Kaczmarz for tensor linear systems, On a fast deterministic block Kaczmarz method for solving large-scale linear systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Round-off error analysis of iterations for large linear systems
- On some methods for entropy maximization and matrix scaling
- Characterization of linear stationary iterative processes for solving a singular system of linear equations
- An iterative method for solving partitioned linear equations
- Algorithms for projection methods for solving linear systems of equations
- Projection method for solving a singular system of linear equations and its applications
- Convergent Powers of a Matrix with Applications to Iterative Methods for Singular Linear Systems
- Consistency and Splittings
- Accelerated projection methods for computing pseudoinverse solutions of systems of linear equations
- Numerical Methods for Computing Angles Between Linear Subspaces
- On the Solution of Singular and Semidefinite Linear Systems by Iteration
- The Kantorovich and Some Related Inequalities
- Projection Methods for Solving Sparse Linear Systems
- Two Algorithms Related to the Method of Steepest Descent
- The method of projections for finding the common point of convex sets
- On the Convergence of Two-Stage Iterative Processes for Solving Linear Equations