Convergence analysis for Kaczmarz-type methods in a Hilbert space framework

DOI10.1016/j.laa.2015.03.028zbMath1312.65051OpenAlexW2050916698MaRDI QIDQ2347471

Wei-Qi Zhou, Peter Oswald

Publication date: 27 May 2015

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.03.028

zbMATH Keywords

condition numberGauss-Seidel iterationrandomizedsubspace correctionalternating directions methodleast-squares problemsPOCS algorithms

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) 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 (14)

Randomized Iterative Methods for Linear Systems ⋮ Rates of convergence of randomized Kaczmarz algorithms in Hilbert spaces ⋮ Convergence rates for Kaczmarz-type algorithms ⋮ Properties and applications of a conjugate transform on Schatten classes ⋮ Triangular truncation and its extremal matrices ⋮ A linearly convergent doubly stochastic Gauss-Seidel algorithm for solving linear equations and a certain class of over-parameterized optimization problems ⋮ Stochastic Reformulations of Linear Systems: Algorithms and Convergence Theory ⋮ A Sampling Kaczmarz--Motzkin Algorithm for Linear Feasibility ⋮ Random reordering in SOR-type methods ⋮ Schwarz iterative methods: infinite space splittings ⋮ The Kaczmarz algorithm, row action methods, and statistical learning algorithms ⋮ Notes on flexible sequential block iterative methods ⋮ Stochastic subspace correction methods and fault tolerance ⋮ Randomized and fault-tolerant method of subspace corrections

Uses Software

• Regularization tools

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Greedy and randomized versions of the multiplicative Schwarz method
• Randomized block Kaczmarz method with projection for solving least squares
• Acceleration of randomized Kaczmarz method via the Johnson-Lindenstrauss lemma
• Block-iterative methods for consistent and inconsistent linear equations
• Randomized Kaczmarz solver for noisy linear systems
• A randomized Kaczmarz algorithm with exponential convergence
• On the convergence rate of SOR: A worst case estimate
• On the abstract theory of additive and multiplicative Schwarz algorithms
• Interlacing families. II: Mixed characteristic polynomials and the Kadison-Singer problem
• Paved with good intentions: analysis of a randomized block Kaczmarz method
• Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Fundamentals of Computerized Tomography
• Randomized Extended Kaczmarz for Solving Least Squares
• Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems
• Optimal scaling parameters for sparse grid discretizations
• Randomized Methods for Linear Constraints: Convergence Rates and Conditioning
• The Kadison–Singer Problem in mathematics and engineering
• On Diagonally Relaxed Orthogonal Projection Methods
• Iterative Methods by Space Decomposition and Subspace Correction
• The method of alternating projections and the method of subspace corrections in Hilbert space
• On Projection Algorithms for Solving Convex Feasibility Problems
• A Matrix Inequality
• Best approximation in inner product spaces

This page was built for publication: Convergence analysis for Kaczmarz-type methods in a Hilbert space framework