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Computing the extremal positive definite solutions of a matrix equation. (English) Zbl 0856.65044
An implementation of a well-known algorithm is proposed for finding extremal positive definite solutions of the matrix equation $$X+A^*X^{-1}A=I$$. The convergence rate is analyzed. Then a new algorithm is presented. This algorithm avoids matrix inversions.

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