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[1] Cai Jing, Chen Jianlong,. Some new bound estimates of the Hermitian positive definitesolutions of the nonlinear matrix equation Xss+A*X-tA=Q [J]. Journal of Southeast University (English Edition), 2019, 35 (1): 142-146. [doi:10.3969/j.issn.1003-7985.2019.01.020]
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Some new bound estimates of the Hermitian positive definitesolutions of the nonlinear matrix equation Xss+A*X-tA=Q()
非线性矩阵方程 Xss+A*X-tA=Q的Hermitian 正定解的界的新估计
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
35
Issue:
2019 1
Page:
142-146
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2019-03-30

Info

Title:
Some new bound estimates of the Hermitian positive definitesolutions of the nonlinear matrix equation Xss+A*X-tA=Q
非线性矩阵方程 Xss+A*X-tA=Q的Hermitian 正定解的界的新估计
Author(s):
Cai Jing1;  2;  Chen Jianlong1
1School of Mathematics, Southeast University, Nanjing 211189, China
2School of Science, Huzhou University, Huzhou 313000, China
蔡静1;  2;  陈建龙1
1东南大学数学学院, 南京211189; 2湖州师范学院理学院, 湖州313000
Keywords:
nonlinear matrix equation;  Hermitian positive definite solution;  solution bound;  matrix inequality
非线性;  矩阵方程;  Hermitian正定解;  解的界;  矩阵不等式
PACS:
O241.5
DOI:
10.3969/j.issn.1003-7985.2019.01.020
Abstract:
The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s, t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s, t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.
研究了非线性矩阵方程Xss+A*X-tA=Q的Hermitian正定解的范围和存在条件, 其中A为n 阶非奇异复矩阵, Q为n阶Hermitian正定矩阵, 参数s, t>0.基于矩阵几何理论、相关矩阵不等式和线性代数技术, 针对参数s, t的不同取值范围, 给出了Hermitian正定解的存在区间和方程可解的必要条件.比较已有的相关结果, 所给出的Hermitian正定解的上界和下界估计更加精准, 适用范围更广.

References:

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Memo

Memo:
Biographies: Cai Jing(1975—), female, doctor, associate professor, huzhoucaijing@163.com; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371089), the China Postdoctoral Science Foundation(No.2016M601688).
Citation: Cai Jing, Chen Jianlong.Some new bound estimates of the Hermitian positive definite solutions of the nonlinear matrix equation Xss+A*X-tA=Q[J].Journal of Southeast University(English Edition), 2019, 35(1):142-146.DOI:10.3969/j.issn.1003-7985.2019.01.020.
Last Update: 2019-03-20