摘要
基于求线性代数方程组的共轭梯度法的思想,建立一种求Lyapunov矩阵方程的双反对称解的迭代算法,对任意给定的初始双反对称矩阵,算法能够在有限步迭代计算后得到矩阵方程的极小范数双反对称解,同时在上述解集中也可得出指定矩阵的最佳逼近双反称矩阵.数值算例表明,迭代算法是有效的.
On the base of conjugate gradient method of solving linear algebraic equations,.in this paper,an iterative method is presented to find the anti-bisymmetric solution of Lyapunov matrix equation.By this iterative method,for any initial anti-bisymmetric matrix,a solution can be obtained within finite iterative steps,and the solution with least-norm can be obtained by choosing a special initial matrix.In addition,the expression of its optimal approximation solution to a given matrix can be obtained.The numerical examples show that the iterative algorithm is quite efficient.
出处
《数学的实践与认识》
北大核心
2015年第6期273-280,共8页
Mathematics in Practice and Theory
基金
陕西省电子信息系统综合集成重点实验室基金资助
关键词
矩阵方程
迭代算法
极小范数解
双反对称矩阵
最佳逼近
matrix equation
iterative method
least-norm solution
anti-bisymmetric matrix
optimal approximation
