Modified generalised successive over-relaxation method for augmented linear systems

Shengkun Li, Ting-Zhu Huang, Li-Tao Zhang


We introduce here a modified generalised successive over-relaxation (MGSOR) method to solve augmented linear systems. We prove that the MGSOR method converges to the unique solution of the linear system for a loose restriction on three parameters. Finally, a numerical example illustrates the effectiveness of the MGSOR iteration method which outperforms the modified SOR-like method and the generalised successive over-relaxation method.

  • Z. Z. Bai, B. N. Parlett, Z. Q. Wang, On generalized successive overrelaxation methods for augmented linear systems, Numer. Math., 102(2005), 1--38, doi:10.1007/s00211-005-0643-0
  • G. H. Golub, X. Wu, J. Y. Yuan, SOR-like methods for augmented systems, BIT, 41(2001), 71--85, doi:10.1023/A:1021965717530
  • X. H. Shao, Z. Li, C. J. Li, Modified SOR-like method for the augmented system, Int. J. Comput. Math., 84(2007), 1653--1662, doi:10.1080/00207160601117313
  • F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods, Springer--Verlag, New York and London, 1991.
  • M. Fortin, R. Glowinski, Augmented Lagrangian Methods, Applications to the Numerical Solution of Boundary Value Problems, North--Holland, Amsterdam, 1983.
  • M. T. Darvishi, P. Hessari, Symmetric SOR method for augmented systems, Appl. Math. Comput., 183(2006), 409--415, doi:10.1016/j.amc.2006.05.094
  • D. M. Young, Iterative Solution for Large Linear Systems, Academic Press, New York, 1971.


SOR-like method; GSOR method; MGSOR method; augmented linear system; iterative method

Full Text:



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.