J4 ›› 2013, Vol. 48 ›› Issue (4): 65-71.

• Articles • Previous Articles     Next Articles

Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method

XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1   

  1. 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
    2. Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, Shaanxi, China
  • Received:2012-05-15 Online:2013-04-20 Published:2013-04-16

Abstract:

 The optimal scaling matrix and the estimates of some amounts of  M-1N are used to discuss the convergence of the extrapolated Gauss-Seidel iteration methods and the relationship between them and H-matrices. Several equivalent conditions for the Hmatrices based on the extrapolated Gauss-Seidel and the Gauss-Seidel iterative methods are obtained. And the convergence results of the Gauss-Seidel and the extrapolated Gauss-Seidel iterative methods are given for the strictly diagonally dominant matrices, the irreducible diagonally dominant matrices and the Stieltjes matrices.

Key words:  H-matrix; Gauss-Seidel iterative method; extrapolated Gauss-Seidel iterative method; optimal scaling matrix; spectral radius

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