稀疏线性方程组的一种预处理并行算法

A parallel preconditioned method for sparse linear systems

给出了一种求解系数矩阵为稀疏对称正定矩阵的线性方程组的预处理共轭梯度法的并行算法.该方法提出了迭代法的预处理模式.基于此思想,首先给出预条件子M,然后构造并行迭代求解预处理方程组的迭代格式,进而使用共轭梯度法并行求解.通过数值试验,与直接使用共轭梯度法及传统的预处理共轭梯度方法(迭代1次)相比,该方法提高了收敛速度,同时具有很好的并行性.

A parallel preconditioned conjugate gradient method is proposed in this manuscript to solve linear systems with a sparse, symmetric and positive coefficient matrix. The preconditioned idea of iteration method is derived. First, given the preconditioner M, the iterative method was constructed to solve preconditioned systems in a parallel form. Then, conjugate gradient method is applied to solve the linear systems in a parallel way. Compared with the solution of directly implementing conjugate gradient method and traditional preconditioned conjugate gradient meth- od （iterating one time） through numerical experiments, the proposed method does improve the convergence rate of conjugate gradient method, with a well parallelisro.