在具有局部内存与共享主存的并行机上并行求解线性方程组

PARALLELLY SOLVING LINEAR SYSTEMS ON A HIERARCHY MEMORY MULTIPROCESSOR

求解线性方程组是解许多问题的核心,因此有效地求解线性方程组在科学与工程计算中是非常重要的.并行计算机的问世,使求解问题的速度和解题规模大幅度地提高.同时也使计算方法产生了变化.在传统的串行机上,LINPACK数学软件是求解线性方程组的有效软件包,然而在并行机上求解此问题,就需要设计出适合该机的并行算法.算法的优劣会对并行机的效率产生很大的影响,这里考虑的重点是并行计算一矩阵A的LU分解,亦即存在一排列矩阵P,使AP=LU.由于是在具有局部内存与共享主存的并行机上求解问题,因此算法的设计要有分布式计算的特点。

In this paper, the parallel implementation of solving a system of dense linear algebraic equations on a parallel computer is proposed, which has shared memory and local memory. The parallel computer's architecture is considered and the function of local memory is used. Therefore, with this method each processor does not need to wait for data exchange. Finally, the numerical results show that the efficiency of the method for solving linear algebraic equations is over 98%.