线性方程组并行迭代解法的新思路

针对求解大型线性方程组,利用改进后的MGS方法和分治策略,给出了一种求解任意相容性线性方程组通解或不相容性线性方程组最小二乘解通解的并行数值方法,分析了该方法的复杂性和数值稳定性,探讨其基于MIMD分布式存储或分布共享存储模型的消息传递并行算法的设计方法。

A New Approach to Parallel Method for System of Linear Equations

This paper improves Gram-Schmidt's orthogonal reduction method(MGS)and then proceed to put forward a parallel numerical method to solve the general solution of arbitrary consistent system of linear equations or the general solution of the least squares solution of arbitrary inconsistent system of linear equations by the improved MGS method and the dividing-conquering strategy,also discusses its computational complexity and its numerical stability,so its corresponding message passing parallel programming rules based on the model with MIMD computer of the distributed memory or the distributed-shared memory.