On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems

DOI10.4208/eajam.100821.251121zbMath1481.65067OpenAlexW4213348416MaRDI QIDQ5061744

Lu Wang, Galina V. Muratova, Zhong Zhi Bai

Publication date: 14 March 2022

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/eajam.100821.251121

zbMATH Keywords

relaxationsystem of linear equationsconvergence propertyrandomized Kaczmarz methodaugmented linear system

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical mathematical programming methods (65K05) Convex programming (90C25) Linear equations (linear algebraic aspects) (15A06)

Related Items (8)

On randomized partial block Kaczmarz method for solving huge linear algebraic systems ⋮ A semi-randomized Kaczmarz method with simple random sampling for large-scale linear systems ⋮ On adaptive block coordinate descent methods for ridge regression ⋮ Randomized Kaczmarz iteration methods: algorithmic extensions and convergence theory ⋮ On the convergence of randomized and greedy relaxation schemes for solving nonsingular linear systems of equations ⋮ On multi-step randomized extended Kaczmarz method for solving large sparse inconsistent linear systems ⋮ On convergence rates of Kaczmarz-type methods with different selection rules of working rows ⋮ Multi-step greedy Kaczmarz algorithms with simple random sampling for solving large linear systems

Uses Software

• SparseMatrix

Cites Work

• A randomized Kaczmarz algorithm with exponential convergence
• On convergence rate of the randomized Kaczmarz method
• On relaxed greedy randomized Kaczmarz methods for solving large sparse linear systems
• A new greedy Kaczmarz algorithm for the solution of very large linear systems
• On convergence rate of the randomized Gauss-Seidel method
• Variant of greedy randomized Kaczmarz for ridge regression
• On partially randomized extended Kaczmarz method for solving large sparse overdetermined inconsistent linear systems
• Paved with good intentions: analysis of a randomized block Kaczmarz method
• Randomized Extended Kaczmarz for Solving Least Squares
• The university of Florida sparse matrix collection
• Convergence Properties of the Randomized Extended Gauss--Seidel and Kaczmarz Methods
• On Greedy Randomized Kaczmarz Method for Solving Large Sparse Linear Systems
• On Greedy Randomized Augmented Kaczmarz Method for Solving Large Sparse Inconsistent Linear Systems
• Matrix Analysis and Computations
• Tight upper bounds for the convergence of the randomized extended Kaczmarz and Gauss–Seidel algorithms
• On greedy randomized coordinate descent methods for solving large linear least‐squares problems

This page was built for publication: On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems