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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()
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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
Author(s):
Cai Jing1;  2;  Chen Jianlong1
1School of Mathematics, Southeast University, Nanjing 211189, China
2School of Science, Huzhou University, Huzhou 313000, China
Keywords:
nonlinear matrix equation;  Hermitian positive definite solution;  solution bound;  matrix inequality
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.

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