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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
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References:
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