Greed works: An improved analysis of sampling Kaczmarz--Motzkin
Stochastic iterative algorithms have gained recent interest in machine learning and signal
processing for solving large-scale systems of equations, Ax=b. One such example is the …
processing for solving large-scale systems of equations, Ax=b. One such example is the …
On adaptive stochastic heavy ball momentum for solving linear systems
The stochastic heavy ball momentum (SHBM) method has gained considerable popularity
as a scalable approach for solving large-scale optimization problems. However, one …
as a scalable approach for solving large-scale optimization problems. However, one …
Sharp analysis of sketch-and-project methods via a connection to randomized singular value decomposition
M Dereziński, E Rebrova - SIAM Journal on Mathematics of Data Science, 2024 - SIAM
Sketch-and-project is a framework which unifies many known iterative methods for solving
linear systems and their variants, as well as further extensions to nonlinear optimization …
linear systems and their variants, as well as further extensions to nonlinear optimization …
On the Kaczmarz methods based on relaxed greedy selection for solving matrix equation AXB= C
NC Wu, CZ Liu, Q Zuo - Journal of Computational and Applied Mathematics, 2022 - Elsevier
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 …
representative among iterative algorithms due to its simplicity and efficiency. Based on the …
[HTML][HTML] Faster randomized block sparse Kaczmarz by averaging
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 …
sparse solutions of linear systems of equations and uses sequential updates, and thus, does …
On convergence rates of Kaczmarz-type methods with different selection rules of working rows
ZZ Bai, L Wang - Applied Numerical Mathematics, 2023 - Elsevier
The Kaczmarz method is a classical while effective iteration method for solving very large-
scale consistent systems of linear equations, and the randomized Kaczmarz method is an …
scale consistent systems of linear equations, and the randomized Kaczmarz method is an …
Randomized Douglas–Rachford Methods for Linear Systems: Improved Accuracy and Efficiency
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 …
intersection of two closed convex sets (feasibility problem). However, the method converges …
Adaptive Bregman-Kaczmarz: An approach to solve linear inverse problems with independent noise exactly
We consider the block Bregman-Kaczmarz method for finite dimensional linear inverse
problems. The block Bregman-Kaczmarz method uses blocks of the linear system and …
problems. The block Bregman-Kaczmarz method uses blocks of the linear system and …
A weighted randomized Kaczmarz method for solving linear systems
S Steinerberger - Mathematics of Computation, 2021 - ams.org
The Kaczmarz method for solving a linear system $ Ax= b $ interprets such a system as a
collection of equations $\left\langle a_i, x\right\rangle= b_i $, where $ a_i $ is the $ i $-th row …
collection of equations $\left\langle a_i, x\right\rangle= b_i $, where $ a_i $ is the $ i $-th row …
On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems
J Zhang, J Guo - Applied Numerical Mathematics, 2020 - Elsevier
The greedy randomized coordinate descent (GRCD) method is an effective iterative method
for solving large linear least-squares problems. In this work, we construct a class of relaxed …
for solving large linear least-squares problems. In this work, we construct a class of relaxed …