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文章摘要
陈世军.Riccati矩阵方程的对称自反解的迭代算法*[J].海南大学学报编辑部:自然科学版,2019,37(2):.
Riccati矩阵方程的对称自反解的迭代算法*
An Iterative Method to Find Symmetric Matrix Solutionsand Reflexive Matrix Solutions of Riccati Matrix Equation
投稿时间:2019-01-08  修订日期:2019-01-16
DOI:10.15886/j.cnki.hdxbzkb.2019.0016
中文关键词: Riccati矩阵方程;对称解;自反解;修正共轭梯度法
英文关键词: Riccati matrix equation; symmetric matrix solutions; reflexive matrix solutions; modified conjugate method.
基金项目:2018年福建省教育厅中青年教育科研项目(JZ180190);福建工程学院应用技术学院2018年科研项目(YYJS-JB1808)
作者单位E-mail
陈世军 福建工程学院应用技术学院 2101751487@qq.com 
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中文摘要:
      研究了Riccati矩阵方程的对称自反解解问题,用牛顿算法将Riccati矩阵方程的对称自反解转化为线性矩阵方程的对称自反解,采用变形共轭梯度算法(MCG)解决了线性矩阵方程的对称自反解或者是最小二乘解问题.算例表明,该算法是有效的.
英文摘要:
      An iterative method is studied to solve for symmetric matrix solutions and reflexive matrix solutions of Riccati matrix equation. First, Nentow’s method is applied for computing the symmetric matrix solutions and reflexive matrix solutions of the Riccati matrix equation, a linear matrix equation will be dericed, Then an MCG iterative method is established to solve for symmetric matrix solutions and reflexive matrix solutions or symmetric matrix solutions and reflexive matrix solutions least-squares solutions of the Riccati matrix equation. Numerical examples show that the method is effective.
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