## Properties of positive definite solutions of the equation $$X+A^*X^{-2}A=I$$.(English)Zbl 0935.65041

Summary: We discuss some properties of a positive definite solution of the matrix equation $$X+ A^*X^{-2}A= I$$. Two effective iterative methods for computing a positive definite solution of this equation are proposed. Necessary and sufficient conditions for the existence of a positive definite solution are derived. Numerical experiments are executed with these methods.

### MSC:

 65F30 Other matrix algorithms (MSC2010) 65F10 Iterative numerical methods for linear systems 15A24 Matrix equations and identities
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### References:

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