Bulletin of the Korean Mathematical Society ( Vol.48 NO.2 / 2011 ) Title Preconditioned Gauss-Seidel iterative method for $Z$-matrices linear systems(ENG) Author Hailong Shen ,Xinhui Shao ,Zhenxing Huang ,Chunji Li  MSC 65F08 Publication Page 303-314 Page Abstract 1. Introduction 2. Basic results 3. New preconditioned iterative method and convergence analysis 4. Numerical examples 5. Conclusion Own Status Keyword Gauss-Seidel iterative method, preconditioned method, $Z$-matrix, diagonal dominant matrix Note Summary 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+Sleft( alpha ight) $ 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+Sleft( alpha ight) +ar{K}left( eta ight) $ 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 cite{9} theoretically. Numerical examples show the effectiveness of our algorithm. Attach [PDF]