线性方程组的并行算法及在Transputer系统上的实现

A Parallel Algorithm of Solving Linear Equations and Implementation on Multitransputer Systems

在“一种有效的多Transputer系统的并行算法——ABC法”一文的基础上,本文进一步研究将ABC法用于变带宽矩阵线性方程组的求解问题,对线性方程组的系数矩阵采用了逐行一维存储方式,提出了相应的并行Gauss消元法,给出了该算法的效率.分析结果表明,带宽越大方程阶数越高,这种算法的效率就越高。因此本算法适用于高阶的大带宽线性方程组的求解问题. 根据本文的算法,编制了线性方程组的并行求解程序,并分别在一个、二个和四个T414系统上做了若干算例,结果表明本文分析的结论是正确的。

Based on the paper 'An Efficient Parallel Algorithm for Multitransputer Systems: ABC Method' written by the first two authers previously, the ABC method is used to solve the linear algebraic equations with variably banded coefficient matrix. The elements of the coefficient matrix are stored with a one-dimensional array, and the Parallal Gauss eliminating algorithm is proposed. The algorithm complexity, speedup and efficiency are analyzed. The results show that the wider the band and the greater the order of the equations, the higher the efficiency of the algorithm. Therefore, the algorithm is suited to linear equations of high order and wide band.A program implementing the algorithm proposed in this paper on multitransputer systems is written, and several examples are made separately on one, two and four T414 systems. It shows that the results of the analysis in this paper are correct.