| 一类非线性矩阵方程的正定解 |
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| 引用本文： | 房亮,刘三阳. 一类非线性矩阵方程的正定解[J]. 浙江大学学报(理学版), 2019, 46(1): 1-8. DOI: 10.3785/j.issn.1008-9497.2019.01.001 |
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| 作者姓名： | 房亮 刘三阳 |
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| 作者单位： | 西安电子科技大学 数学与统计学院，陕西 西安 710071 |
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| 基金项目： | 国家自然科学基金资助项目（61877046）；基金项目:陕西省自然科学基础研究计划项目(2017JM1001)；中央高校基本科研业务费项目（JBX180714）． |
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| 摘 要： | 讨论非线性矩阵方程X+∑i=1mAi*X-1Ai-∑j=1nBj*X-1Bj=Q的Hermite正定解及其扰动问题。提出了该方程存在唯一正定解的充分条件，给出了迭代解法。讨论了唯一正定解的扰动问题，给出了上界估计，得到了唯一正定解的Rice条件数的显式表达式，并用数值例子对所得结果进行了验证。
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| 关 键 词： | 非线性矩阵方程 Hermite正定解 扰动分析 |
| 收稿时间： | 2018-03-29 |
On positive definite solution of a class of nonlinear matrix equations. |
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| FANG Liang,LIU Sanyang. On positive definite solution of a class of nonlinear matrix equations.[J]. Journal of Zhejiang University(Sciences Edition), 2019, 46(1): 1-8. DOI: 10.3785/j.issn.1008-9497.2019.01.001 |
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| Authors: | FANG Liang LIU Sanyang |
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| Affiliation: | School of Mathematics and Statistics, Xidian University, Xi'an 710126, China |
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| Abstract: | The positive definite solutions of a class of nonlinear matrix equation X+∑i=1mAi*X-1Ai-∑j=1nBj*X-1Bj=Q are addressed. Some sufficient conditions for the existence and uniqueness of the positive definite solution to such equations are established. An iterative method for the unique positive definite solution is provided. Perturbation analysis is also conducted. An estimation bound and the explicit expression of Rice condition number of the unique positive definite solution are derived. Several numerical examples are given to illustrate the effectiveness of the above theoretical results. |
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| Keywords: | nonlinear matrix equation Hermite positive definite solution perturbation analysis |
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