| 一类广义Riccati矩阵方程对称解的双迭代算法 |
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| 引用本文： | 张凯院,宋卫红,王娇.一类广义Riccati矩阵方程对称解的双迭代算法[J].数值计算与计算机应用,2013(4):286-294. |
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| 作者姓名： | 张凯院 宋卫红 王娇 |
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| 作者单位： | 西北工业大学应用数学系,西安710072 |
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| 基金项目： | 国家自然科学基金（11071196）. |
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| 摘 要： | 研究了一类广义系统控制理论导出的Riccati矩阵方程对称解的数值计算方法．运用牛顿算法将Riccati矩阵方程的对称解问题转化为线性矩阵方程的对称解或者对称最小二乘解问题，采用修正共轭梯度法解决导出的线性矩阵方程的对称解问题，可建立求Riccati矩阵方程对称解的双迭代算法．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 对称解 牛顿算法 修正共轭梯度法 双迭代算法 |
A DOUBLE ITERATIVE ALGORITHM FOR SYMMETRIC SOLUTION OF GENERALIZED RICCATI MATRIX EQUATION |
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| Zhang Kaiyuan Song Weihong Wang Jiao.A DOUBLE ITERATIVE ALGORITHM FOR SYMMETRIC SOLUTION OF GENERALIZED RICCATI MATRIX EQUATION[J].Journal on Numerical Methods and Computer Applications,2013(4):286-294. |
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| Authors: | Zhang Kaiyuan Song Weihong Wang Jiao |
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| Affiliation: | Zhang Kaiyuan Song Weihong Wang Jiao (Dept. of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China) |
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| Abstract: | A new iterative method is studied to find symmetric solution of a generalized Riccati matrix equation arising from the control theory of singular system. When Newton＇s method is applied to find symmetric solution of the Riccati matrix equation, a problem to find the symmetric solution or the symmetric least-square solution of a linear matrix equation will be derived. Then the modified conjugate gradient method is applied to solve the derived linear matrix equation. In this way, a double iterative method is established to solve for symmetric solution of the Riccati matrix equation. The effectiveness of the double iterative method is demonstrated by numerical examples. |
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| Keywords: | Riccati matrix equation Symmetric solution Newton＇s method Modifiedconjugate gradient method Double iterative method |
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