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一类Riccati方程组对称自反解的两种迭代算法

张凯院, 耿小姣, 聂玉峰   

  1. 西北工业大学应用数学系, 西安 710072
  • 收稿日期:2015-06-15 出版日期:2016-04-15 发布日期:2016-05-13
  • 基金资助:

    国家自然科学基金(11471262).

张凯院, 耿小姣, 聂玉峰. 一类Riccati方程组对称自反解的两种迭代算法[J]. 计算数学, 2016, 38(2): 161-170.

Zhang Kaiyuan, Geng Xiaojiao, Nie Yufeng. TWO ITERATIVE ALGORITHMS FOR THE SYMMETRIC REFLEXIVE SOLUTION OF A CLASS OF RICCATI EQUATIONS[J]. Mathematica Numerica Sinica, 2016, 38(2): 161-170.

TWO ITERATIVE ALGORITHMS FOR THE SYMMETRIC REFLEXIVE SOLUTION OF A CLASS OF RICCATI EQUATIONS

Zhang Kaiyuan, Geng Xiaojiao, Nie Yufeng   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
  • Received:2015-06-15 Online:2016-04-15 Published:2016-05-13
针对源于Markov跳变线性二次控制问题中的一类对偶代数Riccati方程组,分别采用修正共轭梯度算法和正交投影算法作为非精确Newton算法的内迭代方法,建立求其对称自反解的非精确Newton-MCG算法和非精确Newton-OGP算法.两种迭代算法仅要求Riccati方程组存在对称自反解,对系数矩阵等没有附加限定.数值算例表明,两种迭代算法是有效的.
Concerning coupled algebraic Riccati equations arising from Markov jump linear-quadratic control problems, two iterative methods called the inexact Newton-MCG algorithm and the inexact Newton-OGP algorithm are proposed for the symmetric reflexive solution of those equations by making use of modified conjugate gradient algorithm and orthogonal projection algorithm as the inner iterative method, respectively. These two iterative algorithms have no other limits to the coefficient matrix except for the existence of symmetric reflexive solution. Numerical experiments confirm these two algorithms are effective.

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