Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS

  • Shen, Hailong (College of Sciences or School of Information Engineering Northeastern University) ;
  • Shao, Xinhui (College of Sciences Northeastern University) ;
  • Huang, Zhenxing (College of Sciences Northeastern University) ;
  • Li, Chunji (Institute of System Science College of Sciences Northeastern University)
  • Received : 2009.06.26
  • Published : 2011.03.31
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Abstract

For Ax = b, it has recently been reported that the convergence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S (${\alpha}$) to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this paper, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S (${\alpha}$) + $\bar{K}({\beta})$ as a preconditioner. We present some comparison theorems, which show the rate of convergence of the new method is faster than the basic method and the method in [7] theoretically. Numerical examples show the effectiveness of our algorithm.

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References

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