On the Two SAOR Iterative Formats for Solving Linear Complementarity Problems

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H.Saberi Najafi 1,* S.A.Edalatpanah 1

1. Department of Applied Mathematics, Islamic Azad university of Lahijan, Iran

* Corresponding author.

DOI: https://doi.org/10.5815/ijitcs.2011.05.03

Received: 10 Jan. 2011 / Revised: 17 Apr. 2011 / Accepted: 23 Jun. 2011 / Published: 8 Nov. 2011

Index Terms

Preconditioning, SAOR methods, linear complementarity problem, convergence, H-matrix


Han et.al have applied two SAOR splitting formats for solving the linear complementarity problem. We improve them by introducing a class of preconditioners based on the SAOR methods. The convergences of the modified methods have been analyzed. We also show the applicability of the methods by numerical example.

Cite This Paper

H.Saberi Najafi, S.A.Edalatpanah, "On the Two SAOR Iterative Formats for Solving Linear Complementarity Problems", International Journal of Information Technology and Computer Science(IJITCS), vol.3, no.5, pp.19-24, 2011. DOI:10.5815/ijitcs.2011.05.03


[1]Murty KG. Linear Complementarity, Linear and Nonlinear Programming[M ]. Heldermann Verlag: Berlin, 1988.

[2]Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming, Theory and algorithms[M ]. Third edition. Hoboken, NJ: Wiley-Interscience, 2006. 

[3]Cottle RW, Pang JS, Stone RE. The Linear Complementarity Problem[M ]. Academic Press: NewYork, 1992. 

[4]Yuan D, Song YZ. Modified AOR methods for linear complementarity problem [J]. Appl. Math. Comput ,2003, 140:53-67.

[5]Bai ZZ , Evans DJ. Matrix multisplitting relaxation methods for linear complementarity Problems [J]. Int. J. Comput. Math ,1997,63:309-326.

[6]Li Y, Dai P, Generalized AOR methods for linear complementarity problem[J]. Appl. Math. Comput 2007,188:7-18.

[7]Han X, Yuan D, Jiang Sh. Two SAOR Iterative Formats for Solving Linear Complementarity Problems[J]. IJITCS 2011, 2, 38-45.

[8]Varga RS. Matrix Iterative Analysis[M ]. second ed., Berlin :Springer; 2000.

[9]Frommer A , Szyld DB. H-splitting and two-stage iterative methods[J]. Numer. Math1992, 63:345–356.

[10]Berman A, Plemmons RJ. Nonnegative Matrices in the Mathematical Sciences[M ]. Academic Press: New York,1979.

[11]Milaszewicz JP. Improving Jacobi and Gauss–Seidel iterations[J]. Linear Algebra Appl 1987, 93: 161–170.

[12]Usui M, Niki H, Kohno T. Adaptive Gauss Seidel method for linear systems[J]. Intern. J. Computer Math 1994, 51:119–125.

[13]Li J.,C. Li, W.The Optimal Preconditioner of Strictly Diagonally Dominant Z-matrix[J]. Acta Mathematicae Applicatae Sinica, English Series. .(2008) DOI: 10.1007/s10255-006-6148-5

[14]SaberiNajafi H, Edalatpanah SA. Some Improvements In PMAOR Method For Solving Linear Systems [J]. J.Info. Comp.Sci ,2011, 6:15-22. 

[15]Hirano H , Niki H. Application of a Preconditioning iterative method to the computation of fluid flow [J]. Numer. Funct. Anal.And Optimiz, 2001,22:405-417.