On the alternating randomized block Kaczmarz method
Abstract
The block Kaczmarz method and its variants are designed for solving the over-determined linear system. They involve iteratively projecting the current point onto the solution space of a subset of constraints. In this work, by alternately dealing with two subproblems (i.e., linear system with multiple right-hand sides) using the block Kaczmarz method, we propose the {\it Alternating Randomized Block Kaczmarz} (ARBK) method to solve the linear matrix equation , which incorporates a randomized index selection scheme to determine the subset of constraints. The convergence analysis reveals that the ARBK method has a linear convergence rate bounded by an explicit expression. Several numerical studies have been conducted to validate the theoretical findings.
Cite
@article{arxiv.2311.00199,
title = {On the alternating randomized block Kaczmarz method},
author = {Nian-Ci Wu and Yang Zhou and Zhaolu Tian},
journal= {arXiv preprint arXiv:2311.00199},
year = {2023}
}