摘要
研究一类双矩阵变量Riccati矩阵方程(R-ME)对称解的数值计算问题.运用牛顿算法求R-ME的对称解时,会导出求双矩阵变量线性矩阵方程的对称解或者对称最小二乘解的问题,采用修正共轭梯度法解决导出的线性矩阵方程约束解问题,可建立求R-ME的对称解的迭代算法.数值算例表明,迭代算法是有效的.
An iterative method is studied to solve for symmetric solutions of a two-variable Riccati matrix equation. First, when Newton＇s method is applied for computing the sym- metric solutions of the Riccati matrix equation, a linear matrix equation will be derived, and we need to find its symmetric solutions or symmetric least-squares solutions. Then, we use the modified conjugate gradient method to solve the derived linear matrix equation. Finally, an iterative method is established to solve for symmetric solutions of the Riccati matrix equation. Numerical examples show that the iterative method is effective.
出处
《应用数学学报》
CSCD
北大核心
2013年第5期831-839,共9页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(11071196)资助项目
关键词
Riccati矩阵方程
对称解
牛顿算法
修正共轭梯度法
迭代算法
Riccati matrix equation
symmetric solutions
Newton＇s method
modified conjugate gradient method
iterative method
