An improved symmetric SOR iterative method for augmented systems

Authors

  • Davod Khojasteh Salkuyeh University of Guilan
  • Somayyeh Shamsi
  • Amir Sadeghi

DOI:

https://doi.org/10.5556/j.tkjm.43.2012.479-490

Keywords:

augmented system, symmetric positive denite, SOR-like, MSSOR, improved SSOR

Abstract

In this paper, the improved symmetric SOR (ISSOR) iterative method is introduced to solve augmented systems. Convergence properties of the proposed method are studied. Some numerical experiments of the ISSOR method are given to compare with that of the well-known SOR-like and MSSOR methods.

Author Biographies

Davod Khojasteh Salkuyeh, University of Guilan

 Faculty ofMathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.

Somayyeh Shamsi

Young Researchers Club, Ardabil branch, Islamic Azad University, Ardabil, Iran.

Amir Sadeghi

Young Researchers Club, Ardabil branch, Islamic Azad University, Ardabil, Iran.

References

O. Axelsson, textit{Iterative solution method, Cambridge University Press, Cambridge, 1996.

Bai Z. Z. Bai, B. N. Parlett and Z. Q. Wang, On generalized successive overrelaxtion methods for augmented systems, Numer. Math. 102 (2005), 1-38

Bjorck A. Bjorck, Numerical methods for least squares problems, SIAM, Philadelphia, PA, 1996.

Scott S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, Second edition, Springer-Verlag, New York ,2002.

Brezzi F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer-Verlag, New York, 1991.

Darvishi M.T. Darvishi and P. Hessari, Symmetric SOR method for augmented systems, Appl. Math. Comput. 183, (2006) 409-415.

Elman H. Elman and D. Silvester, Fast nonsymmetric iteration and preconditioning for Navier-Stokes equations, SIAM J. Sci. Comput. 17 (1996), 33-46.

Golub G.H. Golub, X. Wu, J.Y. Yuan, SOR-like methods for augmented systems, BIT 41(2001), 71-85.

Hadj A. Hadjidimos, Accelerated overrelaxation method, Math. Comput. 32 (1978), 149-157.

Saad Y. Saad, Iterative Methods for Sparse linear Systems, PWS press, New York, 1995.

Varga R. S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.

Wright S. Wright, Stability of augmented system factorizations in interior-point methods,SIAM J. Matrix Anal. Appl. 18 (1997), 191-222.

Wu S. L. Wu, T.Z. Huang and X.L. Zhao, A modified SSOR iterative method for augmented systems,J. Comput. Appl. Math. 228 (2009), 424-433.

Young D.M. Young, Iterative Solution for Large Linear Systems, Academic Press, New York, 1971.

J.Y. Yuan, Iterative methods for generalized least squares problems, Ph.D. Thesis, IMPA,Rio de Janeiro, Brazil, 1993.

J.Y. Yuan, Numerical methods for generalized least squares problems, J. Comput. Appl. Math. 66 (1996), 571-584.

J.Y. Yuan, A.N. Iusem, Preconditioned conjugate gradient methods for generalized least squaresproblems, J. Comput. Appl. Math. 71 (1996), 287-297.

C. J. Zarowski, An introduction to numerical analysis for electrical and computer engineers, John Wiley & Sons, Hoboken, New Jersey, 2004.

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Published

2012-12-31

How to Cite

Khojasteh Salkuyeh, D., Shamsi, S., & Sadeghi, A. (2012). An improved symmetric SOR iterative method for augmented systems. Tamkang Journal of Mathematics, 43(4), 479-490. https://doi.org/10.5556/j.tkjm.43.2012.479-490

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Papers