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**On the positive definite solutions of a nonlinear matrix equation.**
*(English)*
Zbl 1268.15013

Summary: The positive definite solutions of the nonlinear matrix equation \(X^s + A^\ast f(X)A = Q\) are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived. Then, the uniqueness of the Hermitian positive definite solution is studied based on an iterative method proposed in this paper. Lastly, the perturbation analysis for this equation is discussed.

### MSC:

15A24 | Matrix equations and identities |

65F30 | Other matrix algorithms (MSC2010) |

65H10 | Numerical computation of solutions to systems of equations |

15B48 | Positive matrices and their generalizations; cones of matrices |

### Keywords:

positive definite solutions; nonlinear matrix equation; iterative method; perturbation analysis
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\textit{P. Liu} et al., J. Appl. Math. 2013, Article ID 676978, 6 p. (2013; Zbl 1268.15013)

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### References:

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