@article{Zhang2024, 
author = {Ke Zhang and Hong-Yan Yin and Xiang-Long Jiang},
title = {An efficient variant of the greedy block Kaczmarz algorithm for solving large linear systems},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {1},
pages = {2473-2499},
keywords = {linear system, Kaczmarz method, greedy Kaczmarz method, block Kaczmarz method},
url = {https://www.sciopen.com/article/10.3934/math.2024122},
doi = {10.3934/math.2024122},
abstract = {By exploiting the concept of row partitioning, we propose an efficient variant of the greedy block Kaczmarz algorithm for solving consistent large linear systems. The number of blocks is determined a priori through numerical experiments. The new algorithm works with a reduced linear system, which dramatically diminishes the computational overhead per iteration. The theoretical result validates that this method converges to the unique least-norm solution of the linear system. The effectiveness of the proposed algorithm is also justified by comparing it with some block Kaczmarz algorithms in extensive numerical experiments.}
}