Convergence of The Gauss-Seidel Iterative Method

Convergence and Comparison Theorems of the Modified Gauss-Seidel Method

In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M -matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented n...

Preconditioned Gauss-seidel Iterative Method for Z-matrices Linear Systems

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) + K̄ (β) as a preconditioner. We present some com...

Self-adaptive Extrapolated Gauss-Seidel Iterative Methods

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive ...

The Convergence Rate of a Multigrid Method with Gauss-Seidel Relaxation for the Poisson Equation

The convergence rate of a multigrid method for the numerical solution of the Poisson equation on a uniform grid is estimated. The results are independent of the shape of the domain as long as it is convex and polygonal. On the other hand, pollution effects become apparent when the domain contains reentrant corners. To estimate the smoothing of the Gauss-Seidel relaxation, the smoothness is meas...

On the convergence of the block nonlinear Gauss-Seidel method under convex constraints