## What is/are Randomized Kaczmarz?

Randomized Kaczmarz - The sampling Kaczmarz-Motzkin (SKM) method is a generalization of the randomized Kaczmarz and Motzkin methods.^{[1]}, randomized Kaczmarz method).

^{[2]}This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects.

^{[3]}If the linear system is consistent, we remove one of the iteration sequences in the two-subspace randomized extended Kaczmarz method, which approximates the projection of the right-hand side vector onto the orthogonal complement space of the range space of the coefficient matrix, and obtain the generalized two-subspace randomized Kaczmarz method, which is actually a generalization of the two-subspace randomized Kaczmarz method without the assumptions of unit row norms and full column rank on the coefficient matrix.

^{[4]}Our estimates are compared with the upper bounds in Jiao et al (2017 Inverse Problems 33 125012) when RRI is reduced to the standard randomized Kaczmarz method.

^{[5]}The basic processing problem boils down to a sparse system of linear equations that can be addressed by the randomized Kaczmarz (RK) algorithm.

^{[6]}Kaczmarz-type methods, such as the randomized Kaczmarz method, the block Kaczmarz method and the Cimmino method, can be derived from the Kaczmarz method.

^{[7]}Randomized Kaczmarz is a simple iterative method for finding solutions of linear systems $Ax = b$.

^{[8]}By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss--Seidel algorithm, and the doubly stochastic Gauss--Seidel algorithm.

^{[9]}For solving large-scale consistent linear system, a greedy randomized Kaczmarz method with oblique projection and a maximal weighted residual Kaczmarz method with oblique projection are proposed.

^{[10]}One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on single rows of the matrix $A$ at a time.

^{[11]}The capacity achieved by three low-complexity precoders is compared considering a single-cell massive MIMO (M-MIMO) broadcast channel; these linear precoders include the conventional zero-forcing (ZF) beamforming, regularized channel inversion (RCI) precoding, and a precoding version based on the iterative randomized Kaczmarz algorithm (rKA).

^{[12]}Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm.

^{[13]}In this paper, we interpret the randomized extended Kaczmarz and Gauss-Seidel algorithms as specific combinations of the randomized Kaczmarz and Gauss-Seidel algorithms and present refined upper bounds for their convergence.

^{[14]}The variants of randomized Kaczmarz (RK) and randomized Gauss-Seidel (RGS) are distinct iterative algorithms for ridge regression.

^{[15]}The proposed protocols are inspired from the recently developed accelerated variants of the randomized Kaczmarz method - a popular method for solving linear systems.

^{[16]}

## Greedy Randomized Kaczmarz

For solving large-scale consistent linear system, a greedy randomized Kaczmarz method with oblique projection and a maximal weighted residual Kaczmarz method with oblique projection are proposed.^{[1]}Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm.

^{[2]}

## randomized kaczmarz method

, randomized Kaczmarz method).^{[1]}If the linear system is consistent, we remove one of the iteration sequences in the two-subspace randomized extended Kaczmarz method, which approximates the projection of the right-hand side vector onto the orthogonal complement space of the range space of the coefficient matrix, and obtain the generalized two-subspace randomized Kaczmarz method, which is actually a generalization of the two-subspace randomized Kaczmarz method without the assumptions of unit row norms and full column rank on the coefficient matrix.

^{[2]}Our estimates are compared with the upper bounds in Jiao et al (2017 Inverse Problems 33 125012) when RRI is reduced to the standard randomized Kaczmarz method.

^{[3]}Kaczmarz-type methods, such as the randomized Kaczmarz method, the block Kaczmarz method and the Cimmino method, can be derived from the Kaczmarz method.

^{[4]}For solving large-scale consistent linear system, a greedy randomized Kaczmarz method with oblique projection and a maximal weighted residual Kaczmarz method with oblique projection are proposed.

^{[5]}The proposed protocols are inspired from the recently developed accelerated variants of the randomized Kaczmarz method - a popular method for solving linear systems.

^{[6]}

## randomized kaczmarz algorithm

This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects.^{[1]}By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber algorithm, the randomized Kaczmarz algorithm, the randomized Gauss--Seidel algorithm, and the doubly stochastic Gauss--Seidel algorithm.

^{[2]}The capacity achieved by three low-complexity precoders is compared considering a single-cell massive MIMO (M-MIMO) broadcast channel; these linear precoders include the conventional zero-forcing (ZF) beamforming, regularized channel inversion (RCI) precoding, and a precoding version based on the iterative randomized Kaczmarz algorithm (rKA).

^{[3]}Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm.

^{[4]}