| 一类Lyapunov型矩阵方程组的中心对称解及其最佳逼近 |
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| 引用本文： | 陈世军,张凯院. 一类Lyapunov型矩阵方程组的中心对称解及其最佳逼近[J]. 数值计算与计算机应用, 2009, 30(2): 119-129 |
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| 作者姓名： | 陈世军 张凯院 |
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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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| 摘 要： | 建立了求矩阵方程组AiXBi＋GiXDi=Fi（i=1,2）的中心对称解的迭代算法.使用该方法不仅可以判断矩阵方程组是否有中心对称解,而且在有中心对称解时,还能够在有限步迭代计算之后得到矩阵方程组的极小范数中心对称解.同时,也能够在矩阵方程组的中心对称解集合中求得给定矩阵的最佳逼近.
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| 关 键 词： | 矩阵方程组 极小范数中心对称解 迭代算法 最佳逼近 |
CENTRAL SYMMETRIC SOLUTION OF A CLASS LYAPUNOV MATRIX EQUATIONS AND ITS OPTIMAL APPROXIMATION SOLUTION |
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| Chen Shijun,Zhang Kaiyuan. CENTRAL SYMMETRIC SOLUTION OF A CLASS LYAPUNOV MATRIX EQUATIONS AND ITS OPTIMAL APPROXIMATION SOLUTION[J]. Journal on Numerical Methods and Computer Applications, 2009, 30(2): 119-129 |
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| Authors: | Chen Shijun Zhang Kaiyuan |
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| Affiliation: | Chen Shijun Zhang Kaiyuan (Dept. of Applied Mathematics, Northwestern Polytechnical University, Xi＇an 710072, China) |
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| Abstract: | A iterative method is presented to find the central symmetric solution of the matrix equations AiXBi＋GiXDi=Fi（i=1,2）. By this iterative method, the solvability of the equations can be determined automatically, its least-norm central symmetric solution can be got within finite steps. In addition, its optimal approximation solution to a given matrix in a given solution set can be obtained. |
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| Keywords: | matrix equations least-norm central symmetric solution iterative method optimal approximation |
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