The Comparison of the convergence rate with different preconditioners for Linear Systems

  • Aijuan Li School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, PR China
Keywords: Gauss-Seidel iterative, spectral radius, M-matrix, preconditioner

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.

Downloads

Download data is not yet available.

References

J.Y.Yuan. D.D.Zontini, “Comparison theorems of preconditioned Gauss-Seidel methods for

M-matrices,” App.Math.Comput.,V219, pp.1947-1957,2012.

A.D.Gunawardena, S.K.Jain, L.Snyder, “Modified iterative methods for consistent linear

systems,” Linear Algebra Appl., V154-156, pp.123-143,1991.

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.

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.

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.

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.

L.Y.Sun, “A comparison theorem for the SOR iterative method,” J.Comput.Appl.Math.,

V181,pp.336-341,2005.

J.H.Yun, “Comparison results of the preconditioned AOR methods for L-matrices,”

Appl.Math.Comput., V218,pp.3399-3413,2011.

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.

R.S.Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood cliffs.NJ, 1962.

D.M.Young, Iterative solution of large Linear systems. New York, Academic.1971.

Y.T.Li, S.F.Yang, “A multi-parameters preconditioned AOR iterative method for linear systems,” Appl.Math.Comput., V206,pp.465-473,2008.

Published
2021-06-07
How to Cite
Li, A. (2021). The Comparison of the convergence rate with different preconditioners for Linear Systems. IJRDO- Journal of Educational Research, 6(6), 12-21. https://doi.org/10.53555/er.v6i6.4266