Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I
| Autor: | Asmaa M. Al-Dubiban |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Abstract and Applied Analysis, Vol 2015 (2015) |
| Druh dokumentu: | article |
| ISSN: | 1085-3375 1687-0409 |
| DOI: | 10.1155/2015/473965 |
| Popis: | We investigate the nonlinear matrix equation Xr-∑i=1mAi∗X-δiAi=I, where r is a positive integer and δi∈(0,1], for i=1,2,…,m. We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation. A sufficient condition for the equation to have a unique positive definite solution is established. An iterative algorithm is provided to compute the positive definite solutions for the equation and error estimate. Finally, some numerical examples are given to show the effectiveness and convergence of this algorithm. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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