Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61075", author = "Li Jiang and Baoguang Tian", title = "Preconditioned Mixed-Type Splitting Iterative Method For Z-Matrices", abstract = "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 = "Z-matrix, mixed-type splitting iterative method, precondition,comparison theorem, linear system.", volume = "5", number = "2", pages = "169-4", }