中文摘要：

本文结合具有共轭性的一种特殊多分裂与系数矩阵的稀疏性,提出求解系数矩阵为正定矩阵的线性方程组的并行多分裂迭代法.我们的新迭代法与标准迭代法不同点有两个方面：一是在我们的多分裂方法中只要求其中之一是收敛的分裂;二是权矩阵不必预先给出.这在并行计算中是很有效的算法.最后以数值实验验证新方法的有效性和可行性.

英文摘要：

In this paper we present the parallel multisplitting iterative methods for solving positive definite linear systems, which are iterative methods obtained by combining a special multispiitting that has conjugation property and the sparsity of the coefficient matrixA. The new methods are dif- {erent from the standard muitisplitting method in two respects~in our multisplitting there is only one that is required to be convergent and the weighting matrices are not necessarily be known, resulting in algorithms which can be implemented efficiently on parallel computing systems. Convergence is established and numerical experiments are shown.