| 矩阵方程X+A*XqA=I(q＞0)的Hermite正定解 |
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| 引用本文： | 李磊,张玉海.矩阵方程X+A*XqA=I(q＞0)的Hermite正定解[J].山东大学学报(理学版),2006,41(4):32-39. |
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| 作者姓名： | 李磊 张玉海 |
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| 作者单位： | 山东大学,数学与系统科学学院,山东,济南,250100 |
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| 摘 要： | 考虑非线性矩阵方程X+A*XqA=I(q＞0),其中I是n×n阶的单位矩阵，A是n×n阶的复矩阵.推导出矩阵方程Hermite正定解的性质及方程迭代求解，并给出解的惟一性的显式表达式. 以上结果用数值例子来说明.
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| 关 键 词： | 矩阵方程 正定解 迭代方法 |
| 文章编号： | 1671-9352（2006）04-0032-08 |
| 收稿时间： | 2005-06-22 |
| 修稿时间： | 2005年6月22日 |
The Hermitian positive definite solutions of the matrix equation X + A * XqA = I(q＞0) |
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| LI Lei,ZHANG Yu-hai.The Hermitian positive definite solutions of the matrix equation X + A * XqA = I(q＞0)[J].Journal of Shandong University,2006,41(4):32-39. |
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| Authors: | LI Lei ZHANG Yu-hai |
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| Institution: | School of Math. and System Sci., Shandong Univ., Jinan 250100， Shandong, China |
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| Abstract: | Consider the nonlinear matrix equation X+A*XqA=I with q>0，where I is the n×n identity matrix, A is the n×n complex matrix. Some properties of the solution and the basic fixed point iterations for the equation are discussed in some detail, and the explicit formulations about uniqueness of the solution are given.The results are illustratd by numerical examples. |
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| Keywords: | matrix equation positive definite solution iterative method |
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