Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0)
The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbatio...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/575964 |
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| Summary: | The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples. |
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| ISSN: | 1085-3375 1687-0409 |