对称带状矩阵的并行Cholesky分解及相应线性方程组的并行计算

parallel Cholesky Decomposition of Symmetric Banded Matrix and Parallel Computation of Symmetric Equations

大型结构问题所导出的方程组系数矩阵阶数往往非常浩大,传统的串行计算机受存储容量与计算速度限制往往难以处理。本文给出适合寄存器—寄存器加工方式流水线向量机上对称带状矩阵三角分解的并行算法MPLDLT和对称带状线性方程组求解的并行算法MCSA。在YH—1机上通过对实例的计算表明,算法是高效的。当矩阵的阶数仅力1666阶时,算法MPLDLT比相应串行算法计算速度快25倍,算法MCSA比相应串行算法计算速度快47倍。若结合YH—1机的特点,使用向量“链接”技巧,则算法MPLDLT比相应串行算法的计算速度快74倍。

An efficient parallel cholesky decomposition algorithm (MPLDLT) and the parallel computation of symmetric equations (MCSA) are presented on the parallel computer YH-1 with vector registers. Computational results of a model having an order of 1666 show that the calculation speeds of 25 and 47 times faster than the corresponding series algorithms can be obtained by the algorithms MPLDLT and MCSA respectively.