Related papers: A Weighted Randomized Kaczmarz Method for Solving …
We propose a new method for preconditioning Kaczmarz method by sketching. Kaczmarz method is a stochastic method for solving overdetermined linear systems based on a sampling of matrix rows. The standard approach to speed up convergence of…
A greedy randomized augmented Kaczmarz (GRAK) method was proposed in [Z.-Z. Bai and W.-T. WU, SIAM J. Sci. Comput., 43 (2021), pp. A3892-A3911] for large and sparse inconsistent linear systems. However, one has to construct two new index…
In this paper, several row and column orthogonal projection methods are proposed for solving matrix equation $AXB=C$, where the matrix $A$ and $B$ are full rank or rank deficient and equation is consistent or not. These methods are…
In this note we reconsider two known algorithms which both usually converge faster than the randomized Kaczmarz method introduced by Strohmer and Vershynin(2009), but require the additional computation of all residuals of an iteration at…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems,…
The standard randomized sparse Kaczmarz (RSK) method is an algorithm to compute sparse solutions of linear systems of equations and uses sequential updates, and thus, does not take advantage of parallel computations. In this work, we…
Recovering a signal $x^\ast \in \mathbb{R}^n$ from a sequence of linear measurements is an important problem in areas such as computerized tomography and compressed sensing. In this work, we consider an online setting in which measurements…
The randomzied Kaczmarz method, along with its recently developed variants, has become a popular tool for dealing with large-scale linear systems. However, these methods usually fail to converge when the linear systems are affected by heavy…
For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum…
We study Kaczmarz type methods to solve consistent linear matrix equations. We first present a block Kaczmarz (BK) method that employs a deterministic cyclic row selection strategy. Assuming that the associated coefficient matrix has full…
We study how the learning rate affects the performance of a relaxed randomized Kaczmarz algorithm for solving $A x \approx b + \varepsilon$, where $A x =b$ is a consistent linear system and $\varepsilon$ has independent mean zero random…
Randomized linear system solvers have become popular as they have the potential to reduce floating point complexity while still achieving desirable convergence rates. One particularly promising class of methods, random sketching solvers,…
In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the…
The nonlinear Kaczmarz method was recently proposed to solve the system of nonlinear equations. In this paper, we first discuss two greedy selection rules, i.e., the maximum residual and maximum distance rules, for the nonlinear Kaczmarz…
A class of fast greedy block Kaczmarz methods combined with general greedy strategy and average technique are proposed for solving large consistent linear systems. Theoretical analysis of the convergence of the proposed method is given in…
Randomized regularized Kaczmarz algorithms have recently been proposed to solve tensor recovery models with {\it consistent} linear measurements. In this work, we propose a novel algorithm based on the randomized extended Kaczmarz algorithm…
In this paper, we analyze the greedy randomized Kaczmarz (GRK) method proposed in Bai and Wu (SIAM J. Sci. Comput., 40(1):A592--A606, 2018) for solving linear systems. We develop more precise greedy probability criteria to effectively…
The randomized block Kaczmarz (RBK) method is a widely utilized iterative scheme for solving large-scale linear systems. However, the theoretical analysis and practical effectiveness of this method heavily rely on a good row paving of the…
In this technical report we present a Projection onto Convex Sets (POCS) type algorithm for solving systems of linear equations. POCS methods have found many applications ranging from computer tomography to digital signal and image…