Positive definite solution of the matrix equation X=Q+A^H(Iâ−ŠX-C)^(-Î ́)A
نویسندگان
چکیده
We consider the nonlinear matrix equation X = Q+A (I⊗X−C)A (0 < δ ≤ 1), where Q is an n× n positive definite matrix, C is an mn×mn positive semidefinite matrix, I is the m×m identity matrix, and A is an arbitrary mn×n matrix. We prove the existence and uniqueness of the solution which is contained in some subset of the positive definite matrices under the condition that I ⊗Q > C. Two bounds for the solution of the equation are derived. This equation is related to an interpolation problem when δ = 1. Some known results in interpolation theory are improved and extended.
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