PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHOD FOR Z-MATRICES LINEAR SYSTEMS

Abstract. For Ax = b, it has recently been reported that the conver-gence of the preconditioned Gauss-Seidel iterative method which uses a matrix of the type P = I + S () to perform certain elementary row operations on is faster than the basic Gauss-Seidel method. In this pa-per, we discuss the adaptive Gauss-Seidel iterative method which uses P = I + S () + K () 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. 1