Convergence analysis of the preconditioned Gauss-Seidel method for H-matrices

  • Authors:

  • Qingbing Liu;Guoliang Chen;Jing Cai

  • Affiliations:

  • Department of Mathematics, East China Normal University, Shanghai 200062, PR China and Department of Mathematics, Zhejiang Wanli University, Ningbo 315100, PR China;Department of Mathematics, East China Normal University, Shanghai 200062, PR China;Department of Mathematics, East China Normal University, Shanghai 200062, PR China and School of Science, Huzhou Teachers College, Huzhou 313000, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2008

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Abstract

In 1997, Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123] proved that the convergence rate of the preconditioned Gauss-Seidel method for irreducibly diagonally dominant Z-matrices with a preconditioner I+S"@a is superior to that of the basic iterative method. In this paper, we present a new preconditioner I+K"@b which is different from the preconditioner given by Kohno et al. [Toshiyuki Kohno, Hisashi Kotakemori, Hiroshi Niki, Improving the modified Gauss-Seidel method for Z-matrices, Linear Algebra Appl. 267 (1997) 113-123] and prove the convergence theory about two preconditioned iterative methods when the coefficient matrix is an H-matrix. Meanwhile, two novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative methods are given.