一类特殊矩阵方程的并行预处理变形共轭梯度算法

A Parallel Preconditioned Modified Conjugate Gradient Method for a Kind of Matrix Equation

研究了求解一类矩阵方程AXB=C,提出了一种并行预处理变形共轭梯度法.该方法给出一种迭代法的预处理模式.首先给出的预处理矩阵是严格对角占优矩阵,构造并行迭代求解预处理矩阵方程的迭代格式,进而使用变形共轭梯度法并行求解.通过数值试验,预处理变形共轭梯度法与直接使用变形共轭梯度法相比较,该算法不仅有效提高了收敛速度,而且具有很高的并行性.

In view of a parallel algorithm of preconditioned modified conjugate gradient method for solving a kind of matrix equationAXB = C, a preconditioned model was proposed. Based on this thought, firstly the preconditioned matrix was constructed, which was strictly diagonally dominant matrix, secondly the parallel algorithm for preprocessing matrix equation iterative format was formed, and finally the modified conjugate gradient method was used for parallel solving the preconditioned matrix equation. Through numerical experiments, comparing our algorithm with the modified conjugate gradient method, ours has higher parallel efficiency.