摘要
从参数迭代方法出发,建立了求解大型线性矩阵方程AX+XB+CXD+PXQ=F的唯一解的松弛迭代解法.通过矩阵变换和特征值分析,给出了松弛迭代格式收敛的充要条件.同时为了使得迭代速率加快,给出了两种加速动力迭代格式.最后,通过数值示例对文中所述进行了论证,说明所得算法大大提高了收敛速度.
In this paper, based on the parameter iterative method, construct the relaxation method for solving large linear matrix equation AX＋XB＋CXD＋PXQ=F which has a unique solution. And by matrix transformation method and matrix eigenvalue analysis method, also give the sufficient and necessary conditions for the convergence of the relaxation iterative format. At the same time, in order to quickening the convergence rate, give other two dynamical iterative formats. Finally, by a numerical result, illustrate above theory, and improve the rate of convergence.
出处
《陕西科技大学学报（自然科学版）》
2008年第5期145-149,共5页
Journal of Shaanxi University of Science & Technology
关键词
矩阵方程
松弛迭代
参数迭代
matrix equation
relaxation iteration
parameter iterationn
