The Comparison of the convergence rate with different preconditioners for Linear Systems
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Abstract
In this paper, the preconditioned Gauss-Seidel iterative methods are proposed with different
preconditioners. The comparison theorem is obtained under the different preconditioners when the
coefficient matrix A of linear system is a nonsingular M- matrix. This generalizes the result in [1].
Numerical example are given to illustrate our theoretical result.
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References
M-matrices,” App.Math.Comput.,V219, pp.1947-1957,2012.
[2] A.D.Gunawardena, S.K.Jain, L.Snyder, “Modified iterative methods for consistent linear
systems,” Linear Algebra Appl., V154-156, pp.123-143,1991.
[3] D.J.Evans, M.M.Martins, M.E.Trigo, “The AOR iterative method for new preconditioned
linear systems,” J.Comput.Appl.Math. V132, pp.461-466,2001.
[4] H.Kotakemori, K.Harada, M.Morimoto, H.Niki, “A comparison theorem for the iterative
method with the preconditioner（ I Smax),” J.Comput.Appl.Math., V145,pp.373-378,2002.
[5] A.Hadjidioms, D.Noutsos, M.Tzoumas, “More on modifications and improvements of
classical iterative schemes for M-matrices,” Linear Algebra Appl., V364,pp.253-279,2003.
[6] H.Niki, K.Harada, M.Morimoto, M.Sakakihara, “The survey of preconditioners used for
accelerating the rate of convergence in the Gauss-Seidel method,” J.Comput.Appl.Math.,
V164-165,pp.587-600,2004.
[7] L.Y.Sun, “A comparison theorem for the SOR iterative method,” J.Comput.Appl.Math.,
V181,pp.336-341,2005.
[8] J.H.Yun, “Comparison results of the preconditioned AOR methods for L-matrices,”
Appl.Math.Comput., V218,pp.3399-3413,2011.
[9] A.J.Li, “A new preconditioned AOR iterative method and comparison theorems for linear
systems,” IAENG Internationa Journal of Applied Mathematics, V42,pp.161-163,2012.
[10] R.S.Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood cliffs.NJ, 1962.
[11] D.M.Young, Iterative solution of large Linear systems. New York, Academic.1971.
[12]Y.T.Li, S.F.Yang, “A multi-parameters preconditioned AOR iterative method for linear systems,” Appl.Math.Comput., V206,pp.465-473,2008.