相关论文: Refined upper bounds for the convergence of the ra…
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…
The randomized Kaczmarz (RK) method is a well-known approach for solving linear least-squares problems with a large number of rows. RK accesses and processes just one row at a time, leading to exponentially fast convergence for consistent…
The randomized Kaczmarz (RK) algorithm is one of the most computationally and memory-efficient iterative algorithms for solving large-scale linear systems. However, practical applications often involve noisy and potentially inconsistent…
Kaczmarz's alternating projection method has been widely used for solving a consistent (mostly over-determined) linear system of equations Ax=b. Because of its simple iterative nature with light computation, this method was successfully…
We analyze task orderings in continual learning for linear regression, assuming joint realizability of training data. We focus on orderings that greedily maximize dissimilarity between consecutive tasks, a concept briefly explored in prior…
It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices…
Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a…
Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate…
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,…
For solving large consistent linear systems by iteration methods, inspired by the maximum residual Kaczmarz method and the randomized block Kaczmarz method, we propose the maximum residual block Kaczmarz method, which is designed to…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of…
In this work, we shed light on the so-called Kaczmarz method for solving Linear System (LS) and Linear Feasibility (LF) problems from a optimization point of view. We introduce well-known optimization approaches such as Lagrangian penalty…
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…
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…
Randomized Kaczmarz-type methods are widely used for their simplicity and efficiency in solving large-scale linear systems and optimization problems. However, their applicability is limited when dealing with inconsistent systems or…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
The Randomized Kaczmarz method (RK) is a stochastic iterative method for solving linear systems that has recently grown in popularity due to its speed and low memory requirement. Selectable Set Randomized Kaczmarz (SSRK) is an variant of RK…
In this paper, an extension of Kaczmarz method, the Kaczmarz method with oblique projection (KO), is introduced and analyzed. Using this method, a number of iteration steps to solve the over-determined systems of linear equations are…
In [Steinerberger, Q. Appl. Math., 79:3, 419-429, 2021] and [Shao, SIAM J. Matrix Anal. Appl. 44(1), 212-239, 2023], two new types of Kaczmarz algorithms, which share some similarities, for consistent linear systems were proposed. These two…