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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Hindawi Limited
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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doaj-55f68ab9eea34df6a056e68e5a1329142020-11-25T00:34:21ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Dongjie Gao |
| 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 |
| author_facet |
Dongjie Gao |
| author_sort |
Dongjie Gao |
| title |
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_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_sort |
existence and uniqueness of the positive definite solution for the matrix equation x=q+a∗(x^−c)−1a |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2013-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2013/216035 |
| work_keys_str_mv |
AT dongjiegao existenceanduniquenessofthepositivedefinitesolutionforthematrixequationxqaxc1a |
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1725313958212009984 |