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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.

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