中文摘要：

概括连续 overrelaxation (GSOR ) 方法被黄雾， Parlett 和王介绍并且学习[Numer。数学。102 (2005 ) ， pp.1-38 ] 为解决线性方程，和最佳的重复的扩充系统，参数和相应最佳的集中因素确切被获得。在这份报纸，我们进一步估计收缩和 GSOR 方法的半收缩因素。学习的动机是一个重复方法的集中速度被收缩因素然而并非由实际上决定光谱在有限步的重复计算的半径。为非退化的扩充线性系统，在一些限制下面，我们获得包含的参数的收缩域，它保证 GSOR 方法的收缩因素是不到一个。为单个却一致的扩充线性系统，我们也以一种类似的方式获得参数的半收缩领域。最后，我们使用二个数字例子验证理论结果和 GSOR 方法的有效性。[从作者抽象]

英文摘要：

The generalized successive overrelaxation （GSOR） method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102（2005）, pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.