Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A
We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. T...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/216035 |
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| author | Dongjie Gao |
| author_facet | Dongjie Gao |
| author_sort | Dongjie Gao |
| collection | DOAJ |
| description | We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via
variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given. |
| format | Article |
| id | doaj-art-55f68ab9eea34df6a056e68e5a132914 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-55f68ab9eea34df6a056e68e5a1329142025-02-03T06:00:31ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/216035216035Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1ADongjie Gao0Department of Mathematics, Heze University, Heze, Shandong 274015, ChinaWe consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X). We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given.http://dx.doi.org/10.1155/2013/216035 |
| spellingShingle | Dongjie Gao Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A Abstract and Applied Analysis |
| title | Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A |
| title_full | Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A |
| title_fullStr | Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A |
| title_full_unstemmed | Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A |
| title_short | Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A |
| title_sort | existence and uniqueness of the positive definite solution for the matrix equation x q a∗ x c 1a |
| url | http://dx.doi.org/10.1155/2013/216035 |
| work_keys_str_mv | AT dongjiegao existenceanduniquenessofthepositivedefinitesolutionforthematrixequationxqaxc1a |