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Solutions and perturbation estimates for the matrix equation $X^s+A^*X^{-t}A=Q$. (English) Zbl 1179.15015
This paper is concerned with the matrix equation $X^{s}+A^{*} X^{-t}A=Q$, for $s$ and $t$ positive integers, where $Q$ is Hermitian and positive definite. Necessary and sufficient conditions for the existence of a Hermitian and positive definite solution are established. An iterative method for computing the solution and perturbation estimates are also considered. Some numerical examples illustrate the presented theory.

15A24Matrix equations and identities
15A45Miscellaneous inequalities involving matrices
65F30Other matrix algorithms
15B48Positive matrices and their generalizations; cones of matrices
Full Text: DOI
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