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

Liu, Panpan; Zhang, Shugong; Li, Qingchun

J. Appl. Math. 2013, Article ID 676978, 6 p. (2013).

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

References:

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