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The iterative method for solving nonlinear matrix equation $X^{s} + A^{*}X^{-t}A = Q$. (English) Zbl 1131.65039
The author provides necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the nonlinear matrix equation $X^s+A^*X^{-t}A=Q$, where $Q$ is an Hermitian positive definite matrix, $A^*$ is the conjugate transpose of the matrix $A$, and $s,\,t$ are positive integers. In order to compute Hermitian positive definite solutions, an iterative method is derived. In addition, the author also provides a perturbation bound for the Hermitian positive definite solutions. Moreover some numerical examples are also presented.

MSC:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
15A24Matrix equations and identities
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Full Text: DOI
References:
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