@Article{NMTMA-14-714,
author = {Duan , Li-Xiao and Zhang , Guo-Feng},
title = {Variant of Greedy Randomized Gauss-Seidel Method for Ridge Regression},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2021},
volume = {14},
number = {3},
pages = {714--737},
abstract = {<p style="text-align: justify;">The variants of randomized Kaczmarz and randomized Gauss-Seidel algorithms are two effective stochastic iterative methods for solving ridge regression
problems. For solving ordinary least squares regression problems, the greedy randomized Gauss-Seidel (GRGS) algorithm always performs better than the randomized Gauss-Seidel algorithm (RGS) when the system is overdetermined. In this paper, inspired by the greedy modification technique of the GRGS algorithm, we extend
the variant of the randomized Gauss-Seidel algorithm, obtaining a variant of greedy
randomized Gauss-Seidel (VGRGS) algorithm for solving ridge regression problems.
In addition, we propose a relaxed VGRGS algorithm and the corresponding convergence theorem is established. Numerical experiments show that our algorithms
outperform the VRK-type and the VRGS algorithms when $m &gt; n$.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2020-0095},
url = {http://global-sci.org/intro/article_detail/nmtma/19195.html}
}