中文摘要：

明确的问题在这篇论文被论述的为对称、积极的半的一般反复的方法上的集中分析。首先，提出了被精制为为反复的方法的精力标准集中的必要、足够的条件。为条件的一些解说性的例子也被提供。为明确的系统被获得仅仅依靠指导我们为一般连续潜水艇空间修正方法获得集中率身份的纯矩阵操作的为半的 Gauss-Seidel 方法的锋利的集中率身份。为连续潜水艇空间修正方法的集中率身份在本地修正计划拥有的新条件下面被获得本地精力标准集中。集中率估计然后以处于条件出现的准确潜水艇空格解答者和参数被导出。一致集中多，为一个模型问题的格子方法被集中率身份证明。工作能是 regraded 它为 semidfinite 问题的重复方法的集中上的统一并且简化的分析[8,9 ] 。

英文摘要：

The convergence analysis on the general iterative methods for the symmetric and positive semidefinite problems is presented in this paper. First, formulated are refined necessary and sumcient conditions for the energy norm convergence for iterative methods. Some illustrative examples for the conditions are also provided. The sharp convergence rate identity for the Gauss-Seidel method for the semidefinite system is obtained relying only on the pure matrix manipulations which guides us to obtain the convergence rate identity for the general successive subspace correction methods. The convergence rate identity for the successive subspace correction methods is obtained under the new conditions that the local correction schemes possess the local energy norm convergence. A convergence rate estimate is then derived in terms of the exact subspace solvers and the parameters that appear in the conditions. The uniform convergence of multigrid method for a model problem is proved by the convergence rate identity. The work can be regradled as unified and simplified analysis on the convergence of iteration methods for semidefinite problems [8, 9].