Notes on the Hermitian Positive Definite Solutions of a Matrix Equation
The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1≤δi<0 is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. Some proper...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/128249 |
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| author | Jing Li Yuhai Zhang |
| author_facet | Jing Li Yuhai Zhang |
| author_sort | Jing Li |
| collection | DOAJ |
| description | The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1≤δi<0 is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. Some properties of the unique Hermitian positive definite solution are obtained. A residual bound of an approximate solution to the equation is evaluated. The theoretical results are illustrated by numerical examples. |
| format | Article |
| id | doaj-art-221f5b58299540fc9f4e4bc4bfc7957a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-221f5b58299540fc9f4e4bc4bfc7957a2025-02-03T06:00:56ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/128249128249Notes on the Hermitian Positive Definite Solutions of a Matrix EquationJing Li0Yuhai Zhang1School of Mathematics and Statistics, Shandong University, Weihai 264209, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaThe nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1≤δi<0 is investigated. A fixed point theorem in partially ordered sets is proved. And then, by means of this fixed point theorem, the existence of a unique Hermitian positive definite solution for the matrix equation is derived. Some properties of the unique Hermitian positive definite solution are obtained. A residual bound of an approximate solution to the equation is evaluated. The theoretical results are illustrated by numerical examples.http://dx.doi.org/10.1155/2014/128249 |
| spellingShingle | Jing Li Yuhai Zhang Notes on the Hermitian Positive Definite Solutions of a Matrix Equation Journal of Applied Mathematics |
| title | Notes on the Hermitian Positive Definite Solutions of a Matrix Equation |
| title_full | Notes on the Hermitian Positive Definite Solutions of a Matrix Equation |
| title_fullStr | Notes on the Hermitian Positive Definite Solutions of a Matrix Equation |
| title_full_unstemmed | Notes on the Hermitian Positive Definite Solutions of a Matrix Equation |
| title_short | Notes on the Hermitian Positive Definite Solutions of a Matrix Equation |
| title_sort | notes on the hermitian positive definite solutions of a matrix equation |
| url | http://dx.doi.org/10.1155/2014/128249 |
| work_keys_str_mv | AT jingli notesonthehermitianpositivedefinitesolutionsofamatrixequation AT yuhaizhang notesonthehermitianpositivedefinitesolutionsofamatrixequation |