Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 850986, 7 pages
http://dx.doi.org/10.1155/2013/850986
Research Article

Modified Preconditioned GAOR Methods for Systems of Linear Equations

School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

Received 30 January 2013; Accepted 13 May 2013

Academic Editor: Giuseppe Marino

Copyright © 2013 Xue-Feng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. Y. Yuan, “Numerical methods for generalized least squares problem,” Journal of Computational and Applied Mathematics, vol. 66, pp. 571–584, 1996. View at Google Scholar
  2. J.-Y. Yuan and X.-Q. Jin, “Convergence of the generalized AOR method,” Applied Mathematics and Computation, vol. 99, no. 1, pp. 35–46, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. D. Gunawardena, S. K. Jain, and L. Snyder, “Modified iterative methods for consistent linear systems,” Linear Algebra and Its Applications, vol. 154/156, pp. 123–143, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Hadjidimos, “Accelerated overrelaxation method,” Mathematics of Computation, vol. 32, no. 141, pp. 149–157, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. T. Li, C. X. Li, and S. L. Wu, “Improvement of preconditioned AOR iterative methods for L-matrices,” Journal of Computational and Applied Mathematics, vol. 206, pp. 656–665, 2007. View at Google Scholar
  6. J. P. Milaszewicz, “Improving Jacobi and Gauss-Seidel iterations,” Linear Algebra and Its Applications, vol. 93, pp. 161–170, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. S. Varga, Matrix Iterative Analysis, vol. 27, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  8. D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, NY, USA, 1971. View at MathSciNet
  9. M. T. Darvishi and P. Hessari, “On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices,” Applied Mathematics and Computation, vol. 176, no. 1, pp. 128–133, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. Zhou, Y. Song, L. Wang, and Q. Liu, “Preconditioned GAOR methods for solving weighted linear least squares problems,” Journal of Computational and Applied Mathematics, vol. 224, no. 1, pp. 242–249, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. T. Darvishi, P. Hessari, and B.-C. Shin, “Preconditioned modified AOR method for systems of linear equations,” International Journal for Numerical Methods in Biomedical Engineering, vol. 27, no. 5, pp. 758–769, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, vol. 9, Academic Press, New York, NY, USA; Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet