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COMPARISON RESULTS FOR THE PRECONDITIONED GAUSS-SEIDEL METHODS

  • Yun, Jae-Heon (Department of Mathematics College of Natural Sciences Chungbuk National University)
  • Received : 2010.08.30
  • Published : 2012.01.31

Abstract

In this paper, we provide comparison results of several types of the preconditioned Gauss-Seidel methods for solving a linear system whose coefficient matrix is a Z-matrix. Lastly, numerical results are presented to illustrate the theoretical results.

Keywords

References

  1. A. Berman and R. J. Plemmoms, Nonnegative Matrices in The Mathematical Sciences, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994.
  2. D. J. Evans, M. M. Martins, and M. E. Trigo, The AOR iterative method for new preconditioned linear systems, J. Comput. Appl. Math. 132 (2001), no. 2, 461-466. https://doi.org/10.1016/S0377-0427(00)00447-7
  3. A. Gunawardena, S. Jain, and L. Snyder, Modified iterative methods for consistent linear systems, Linear Algebra Appl. 154/156 (1991), 123-143. https://doi.org/10.1016/0024-3795(91)90376-8
  4. T. Kohno, H. Kotakemori, H. Niki, and M. Usui, Improving the modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997), 113-123. https://doi.org/10.1016/S0024-3795(97)80045-6
  5. W. Li, Comparison results for solving preconditioned linear systems, J. Comput. Appl. Math. 176 (2005), no. 2, 319-329. https://doi.org/10.1016/j.cam.2004.07.022
  6. W. Li, A note on the preconditioned Gauss-Seidel (GS) method for linear systems, J. Comput. Appl. Math. 182 (2005), no. 1, 81-90. https://doi.org/10.1016/j.cam.2004.11.041
  7. M. Neumann and R. J. Plemmons, Convergence of parallel multisplitting iterative methods for M-matrices, Linear Algebra Appl. 88/89 (1987), 559-573. https://doi.org/10.1016/0024-3795(87)90125-X
  8. H. Niki, K. Harada, M. Morimoto, and M. Sakakihara, The survey of preconditioners used for accelerating the rate of convergence in the Gauss-Seidel method, J. Comput. Appl. Math. 164/165 (2004), 587-600. https://doi.org/10.1016/j.cam.2003.11.012
  9. L. Sun, A comparison theorem for the SOR iterative method, J. Comput. Appl. Math. 181 (2005), no. 2, 336-341. https://doi.org/10.1016/j.cam.2004.12.007
  10. R. S. Varga, Matrix Iterative Analysis, Springer, Berlin, 2000.
  11. J. H. Yun, A note on the improving modified Gauss-Seidel (IMGS) method, Appl. Math. Comput. 184 (2007), no. 2, 674-679. https://doi.org/10.1016/j.amc.2006.06.067
  12. J. H. Yun, A note on preconditioned AOR method for L-matrices, J. Comput. Appl. Math. 220 (2008), no. 1-2, 13-16. https://doi.org/10.1016/j.cam.2007.07.009

Cited by

  1. ON A FAST ITERATIVE METHOD FOR APPROXIMATE INVERSE OF MATRICES vol.28, pp.2, 2013, https://doi.org/10.4134/CKMS.2013.28.2.407
  2. Comparison theorems of preconditioned Gauss–Seidel methods for M-matrices vol.219, pp.4, 2012, https://doi.org/10.1016/j.amc.2012.08.037