预条件Gauss-Seidel迭代法的收敛性

On convergence of preconditioned Gauss-Seidel iterative method

给出一种预条件Gauss-Seidel迭代法,证明了当系数矩阵A为不可约的Z-矩阵、H-矩阵、正定矩阵时该方法收敛,从而扩展了该方法的适用范围,最后通过数值例子验证所得的主要结论.

The preconditioned Gauss-Seidel iterative method is introduced. It is proved that if the coefficient matrix is an irreducible Z-matrix, H-matrix or positive definite matrix, then the preconditioned Gauss-Seidel iterative method is convergent. Thus it expands the applicable scope of the method. Finally, a simple numerical example shows the validity of the conclusions.