Randomized iterative algorithms have recently been proposed to solve large-scale linear
systems. In this paper, we present a simple randomized extended average block Kaczmarz …

The randomized extended Kaczmarz and Gauss–Seidel algorithms have attracted much
attention because of their ability to treat all types of linear systems (consistent or …

Inspired by the greedy randomized Kaczmarz method, we propose a probability criterion
which can capture subvectors of the residual whose norms are relatively large. According to …

For solving a consistent system of linear equations, the Kaczmarz method is a popular
representative among iterative algorithms due to its simplicity and efficiency. Based on the …

Randomized Kaczmarz-type methods are appealing for large-scale linear systems arising
from big data problems. One of the keys of randomized Kaczmarz-type methods is how to …

The variants of randomized Kaczmarz (RK) and randomized Gauss-Seidel (RGS) are
distinct iterative algorithms for ridge regression. Theoretical convergence rates for these two …

The Douglas–Rachford (DR) method is a widely used method for finding a point in the
intersection of two closed convex sets (feasibility problem). However, the method converges …

Abstract Randomized Kaczmarz, Motzkin Method and Sampling Kaczmarz Motzkin (SKM)
algorithms are commonly used iterative techniques for solving a system of linear inequalities …

We present a new framework for the analysis and design of randomized algorithms for
solving various types of linear systems, including consistent or inconsistent, full rank or rank …

In this note we prove a new theoretical estimate for the convergence rate of the maximal
weighted residual Kaczmarz algorithm for solving a consistent linear system. The estimate …