142
Views
2
CrossRef citations to date
0
Altmetric
Section B

Preconditioned generalized mixed-type splitting iterative method for solving weighted least-squares problemsFootnote

&
Pages 944-963 | Received 22 Jan 2013, Accepted 25 May 2013, Published online: 01 Jul 2013

References

  • A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic, New York, 1979.
  • G.H. Cheng, T.Z. Huang, and S.Q. Shen, Note to the mixed-type splitting iterative method for Z-matrices linear systems, J. Comput. Appl. Math. 220(1–2) (2008), pp. 1–7. doi: 10.1016/j.cam.2007.06.033
  • M.T. Darvishi and P. Hessari, On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176(1) (2006), pp. 128–133. doi: 10.1016/j.amc.2005.09.051
  • P. Lancaster, Theory of Matrix, Academic Press, New York, 1969.
  • C.J. Li and D.J. Evans, Note to the mixed-type splitting method for the positive real linear system, Int. J. Comput. Math. 79(11) (2002), pp. 1201–1209. doi: 10.1080/00207160213943
  • C.J. Li, X.L. Liang, and D.J. Evans, An iterative method for the positive real linear systems, Int. J. Comput. Math. 78(1) (2001), pp. 153–163. doi: 10.1080/00207160108805103
  • M.M. Moghadam and F.P.A. Beik, Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems, Bull. Iranian Math. Soc. 19(2) (2012), pp. 347–365.
  • Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, 2003.
  • H. Shen, X. Shao, and T. Zhang, Preconditioned iterative methods for solving weighted linear least squares problems, Appl. Math. Mech.-Engl. Ed. 33(3) (2012), pp. 375–384. doi: 10.1007/s10483-012-1557-x
  • G.X. Tian, T.Z. Huang, and S.Y. Cui, Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant matrices, J. Comput. Appl. Math. 213(1) (2008), pp. 240–247. doi: 10.1016/j.cam.2007.01.016
  • R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.
  • G. Wang, Y. Du, and F. Tan, Comparison results on preconditioned GAOR methods for weighted linear least squares problems, J. Appl. Math. 2012 (2012), pp. 1–9.
  • G. Wang, H. Wen, and T. Wang, Convergence of GAOR iterative method with strictly α diagonally dominant matrices, J. Appl. Math. 2011 (2011), pp. 1–10.
  • Z.I. Woznicki, Basic comparison theorems for weak and weaker matrix splitting, Electron. J. Linear Algebra 8 (2001), pp. 53–59.
  • M. Wu, L. Wang, and Y. Song, Preconditioned AOR iterative method for linear systems, Appl. Numer. Math. 57(5–7) (2007), pp. 672–685. doi: 10.1016/j.apnum.2006.07.029
  • J.Y. Yuan, Numerical methods for generalized least squares problems, J. Comput. Appl. Math. 66(1) (1996), pp. 571–584. doi: 10.1016/0377-0427(95)00167-0
  • J.Y. Yuan and X.-Q. Jin, Convergence of the generalized AOR method, Appl. Math. Comput. 99(1) (1999), pp. 35–46. doi: 10.1016/S0096-3003(97)10175-8
  • J.H. Yun, Comparison results on the preconditioned GAOR method for generalized least squares problems, Int. J. Comput. Math. 89(15) (2012), pp. 2094–2105. doi: 10.1080/00207160.2012.702898
  • X. Zhou, Y. Song, L. Wang, and Q. Liu, Preconditioned GAOR methods for solving weighted linear least squares problems, J. Comput. Appl. Math. 224(1) (2009), pp. 242–249. doi: 10.1016/j.cam.2008.04.034

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.