| 矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解 |
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| 引用本文： | 廖安平,段雪峰,沈金荣.矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解[J].计算数学,2008,30(4):369-378. |
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| 作者姓名： | 廖安平 段雪峰 沈金荣 |
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| 作者单位： | 长沙学院数学研究所，湖南大学数学与计量经济学院，长沙学院信息与计算科学系 |
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| 基金项目： | 长沙学院科研基金资助
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| 摘 要： | 本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.
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| 关 键 词： | 矩阵方程 正定解 迭代方法 |
HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X+A^{*}X^{-q}A=Q(q\geq 1) |
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| Liao Anping.HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X+A^{*}X^{-q}A=Q(q\geq 1)[J].Mathematica Numerica Sinica,2008,30(4):369-378. |
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| Authors: | Liao Anping |
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| Institution: | 1. Institute of Mathematics, Changsha University, Changsha 410003, China;
2. College of Mathematics and Econometrics, Hunan University, Changsha 410082, China;
3. Department of Information and Computing Science, Changsha University, Changsha 410003, China |
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| Abstract: | The Hermitian positive definite solutions of the matrix equaution $X+A^{*}X^{-q}A=Q(q\geq 1)$ is investigated. Some sufficient conditions and necessary conditions for the existence of positive definite solutions are given. An iterative method for computing Hermitian positive definite
solutions is proposed. Numerical examples are given to illustrate the performance and the effectiveness of the iterative method. |
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| Keywords: | Matrix equation Positive definite solution Iterative method |
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