TY - JOUR
T1 - On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems
AU - Bai , Zhong-Zhi
AU - Wang , Lu
AU - Muratova , Galina V.
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 323
EP - 332
PY - 2022
DA - 2022/02
SN - 12
DO - http://doi.org/10.4208/eajam.100821.251121 
UR - https://global-sci.org/intro/article_detail/eajam/20256.html
KW - System of linear equations, relaxation, augmented linear system, randomized Kaczmarz method, convergence property.
AB - <p style="text-align: justify;">For solving large-scale sparse inconsistent linear systems by iteration methods, we introduce a relaxation parameter in the probability criterion of the greedy
randomized augmented Kaczmarz method, obtaining a class of relaxed greedy randomized augmented Kaczmarz methods. We prove the convergence of these methods and
estimate upper bounds for their convergence rates. Theoretical analysis and numerical
experiments show that these methods can perform better than the greedy randomized
augmented Kaczmarz method if the relaxation parameter is chosen appropriately.</p>