arrow
Volume 12, Issue 2
On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems

Zhong-Zhi Bai, Lu Wang & Galina V. Muratova

East Asian J. Appl. Math., 12 (2022), pp. 323-332.

Published online: 2022-02

Export citation
  • 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.

  • AMS Subject Headings

65F10, 65F20, 65K05, 90C25, 15A06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-12-323, author = {Bai , Zhong-ZhiWang , Lu and Muratova , Galina V.}, title = {On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {2}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100821.251121 }, url = {http://global-sci.org/intro/article_detail/eajam/20256.html} }
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 -

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.

Bai , Zhong-ZhiWang , Lu and Muratova , Galina V.. (2022). On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems. East Asian Journal on Applied Mathematics. 12 (2). 323-332. doi:10.4208/eajam.100821.251121
Copy to clipboard
The citation has been copied to your clipboard