Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

A MIXED-TYPE SPLITTING ITERATIVE METHOD

  • Jiang, Li (Department of Mathematics, Qingdao University of Science and Technology) ;
  • Wang, Ting (Department of Mathematics, Qingdao University of Science and Technology)
  • Received : 2011.03.30
  • Accepted : 2011.06.20
  • Published : 2011.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a preconditioned mixed-type splitting iterative method for solving the linear systems Ax = b is presented, where A is a Z-matrix. Then we also obtain some results to show that the rate of convergence of our method is faster than that of the preconditioned AOR (PAOR) iterative method and preconditioned SOR (PSOR) iterative method. Finally, we give one numerical example to illustrate our results.

Keywords

References

  1. G. Cheng, T. Hunag, S. Shen, Note to the mixed-type splitting iterative method for Z- matrices linear systems, Journal of Computational and Applied Mathematics, 220(2008), 1-7. https://doi.org/10.1016/j.cam.2007.06.033
  2. T. Kohno, H. Kotakemori, Improving the modified Gauss-Seidel method for Z-matrices, Linear Algebra and its Applications, 267(1997), 113-123.
  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 and its Applications, 317(2000), 227-240. https://doi.org/10.1016/S0024-3795(00)00140-3
  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.