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Solutions and perturbation estimates for the matrix equations $X\pm A^*X^{-n}A=Q$. (English) Zbl 1063.15012
The authors consider the two matrix equations $X\pm A^*X^{-n}A=Q$ (where $A$ and $Q$ are complex $m\times m$-matrices) for $X\pm A^*X^{-n}A=Q$ existence of positive definite solutions. They obtain perturbation estimates for these solutions, as well as sufficient conditions for uniqueness of the positive definite solution of the “minus”-equation. The authors illustrate the results by numerical examples.

15A24Matrix equations and identities
Full Text: DOI
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