Year: 2021
Author: Li-Xiao Duan, Guo-Feng Zhang
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 714–737
Abstract
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 $m > n$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0095
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 3 : pp. 714–737
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Randomized algorithms ridge regression greedy randomized Gauss-Seidel randomized Kaczmarz iterative method.
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