針對求解大型線性方程組，利用改進后的MGS方法和分治策略，給出了一種求解任意相容性線性方程組通解或不相容性線性方程組最小二乘解通解的并行數(shù)值方法，分析了該方法的復雜性和數(shù)值穩(wěn)定性，探討其基于MIMD分布式存儲或分布共享存儲模型的消息傳遞并行算法的設(shè)計方法。

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.