Preconditioned Gauss-Seidel iterative method for Z-matrices linear systems
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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(α) 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(α) +[기호](β) 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.
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(α) 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(α) +[기호](β) 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.
참고문헌 (9)
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