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Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices

Authors: Baoguang Tian, Li Jiang


In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Linear System, comparison theorem, Z-matrix, precondition, mixed-type splitting iterative method

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[1] G. Cheng, T. Hunag, S. Shen, Note to the mixed-type splitting iterative method for Z-matrices linear systems, J. Comp. Appl. Math., 220(2008), pp.1-7.
[2] J. Li T. Huang, Preconditioned Methods of Z-matrices, Acta Mathematica Scientia, 25A(2005),pp.5-10.
[3] D.M. Young, Iterative solution of large linear systems, Academic Press, New York, 1971.
[4] R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1981.
[5] W.Li, W.W.Sun, Modified Gauss-Seidel type methods and Jacobi type methods for Z-matrices, Linear Algebra Appl., 317(2000),pp.227-240.
[6] A.Berman, R.J.Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979; SIAM, Philadelphia, PA, 1994.
[7] O.Axelsson, Iterative solution Methods, Cambridge University Press, Cambridge, 1994.