On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems
Year: 2022
Author: Zhong-Zhi Bai, Lu Wang, Galina V. Muratova
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 323–332
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.100821.251121
East Asian Journal on Applied Mathematics, Vol. 12 (2022), Iss. 2 : pp. 323–332
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: System of linear equations relaxation augmented linear system randomized Kaczmarz method convergence property.