| 一类Riccati矩阵方程广义自反解的双迭代算法 |
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| 引用本文： | 张凯院,王娇.一类Riccati矩阵方程广义自反解的双迭代算法[J].数学杂志,2015,35(2):469-476. |
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| 作者姓名： | 张凯院 王娇 |
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| 作者单位： | 西北工业大学应用数学系 |
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| 基金项目： | 国家自然科学基金(11071196) |
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| 摘 要： | 本文研究了一类Riccati矩阵方程广义自反解的数值计算问题.利用牛顿算法将Riccati矩阵方程的广义自反解问题转化为线性矩阵方程的广义自反解或者广义自反最小二乘解问题,再利用修正共轭梯度法计算后一问题,获得了求Riccati矩阵方程的广义自反解的双迭代算法.拓宽了求解非线性矩阵方程的迭代算法.数值算例表明双迭代算法是有效的.
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| 关 键 词： | Riccati矩阵方程 广义自反解 牛顿算法 修正共轭梯度法 双迭代算法 |
| 收稿时间： | 2012/9/3 0:00:00 |
| 修稿时间： | 2012/11/18 0:00:00 |
A DOUBLE ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE SOLUTION OF THE RICCATI MATRIX EQUATION |
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| ZHANG Kai-yuan and WANG Jiao.A DOUBLE ITERATIVE ALGORITHM FOR THE GENERALIZED REFLEXIVE SOLUTION OF THE RICCATI MATRIX EQUATION[J].Journal of Mathematics,2015,35(2):469-476. |
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| Authors: | ZHANG Kai-yuan and WANG Jiao |
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| Institution: | ZHANG Kai-yuan;WANG Jiao;Dept.of Applied Mathematics,Northwestern Polytechnical University; |
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| Abstract: | In this paper, a new iterative method is studied to find the generalized reflexive solution of the Riccati matrix equation. When Newton''s method is applied to find the generalized reflexive solution of the Riccati matrix equation, a problem to find the generalized reflexive solutions or the generalized reflexive least-square solutions of a linear matrix equation will be derived. And then the modified conjugate gradient method is applied to solve the derived linear matrix equation. So a double iterative method is established to find the generalized reflexive solution of the Riccati matrix equation. The iterative algorithm for solving linear matrix equation is promoted. Numerical examples show that the double iterative method is effective. |
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| Keywords: | Riccati matrix equation generalized reflexive solution Newton''s method modified conjugate gradient method double iterative method |
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