Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CONVERGENCE ANALYSIS OF PRECONDITIONED AOR ITERATIVE METHOD

  • Hessari, P. (Department of Mathematics, Chonnam National University) ;
  • Darvishi, M.T. (Department of Mathematics, Razi University) ;
  • Shin, B.C. (Department of Mathematics, Chonnam National University)
  • Received : 2010.05.12
  • Accepted : 2010.08.27
  • Published : 2010.09.25
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Abstract

In this paper, we consider a preconditioned accelerated overrelaxation (PAOR) method to solve systems of linear equations. We show the convergence of the PAOR method. We also give com-parison results when the coefficient matrix is an L- or H-matrix. Finally, we provide some numerical experiments to show efficiency of PAOR method.

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References

  1. Qingbing Liu, Guoliang Chen, Jing Cai, Convergence analysis of the preconditioned Gauss-Seidel method for H-matrices, Computer Math. Appl. 56 (2008) 2048-2053. https://doi.org/10.5831/HMJ.2010.32.3.399
  2. T. Kohno, H. Kotakemori, H. Niki, M. Usui, Improving the Gauss-Seidel method for Z-matrices, Linear Algebra Appl., 267 (1997) 113-123. https://doi.org/10.1016/S0024-3795(97)80045-6
  3. M.T. Darvishi, P. Hessari, B.-Y. Shin, Preconditioned modified AOR method for systems of linear equations, Comm. Numer. Meth. Engng., (in press), doi:10.1002/cnm.1330.
  4. A. Neumaier, On the comparison of H-matrices with M-matrices, Linear Algebra Appl. 83 (1986) 135-141. https://doi.org/10.1016/0024-3795(86)90270-3
  5. C. Li, D.J. Evans, Improving the SOR method, Technical Report 901, Department of computer studies, University of Loughborough, 1994.
  6. A. Berman, R.J. Leramons, Nonnegative matrices in the mathematics sciences, SIAM, Philadelphia, PA, 1994.
  7. R.S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962; Springer Series in Computational Mathematics, vol. 27, Springer-Verlag, Berlin. 2000.
  8. W. Li, W.W. Sun, Modified Gauss-Seidel type methods and Jacobi type methods for Z-matrices, Linear Algebra Appl. 317 (2000) 227-240. https://doi.org/10.1016/S0024-3795(00)00140-3
  9. D.M. Young, Iterative solution for large linear systems, Academic press, New York, (1971).
  10. Y.Z. Song, Comparisons of nonnegative splitting of matrices, Linear Algebra Appl. 154-156 (1991) 433-455. https://doi.org/10.1016/0024-3795(91)90388-D
  11. Y.T. Li, S. Yang, A multi-parameters preconditioned AOR iterative method for linear systems, Appl. Math. Comput. 206 (2008) 465-473. https://doi.org/10.1016/j.amc.2008.09.032

Cited by

  1. CONVERGENCE ANALYSIS OF PRECONDITIONED AOR ITERATIVE METHOD vol.32, pp.3, 2010, https://doi.org/10.5831/HMJ.2010.32.3.399