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We consider the nonlinear matrix equation X = Q+A (I⊗X−C)A (0 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.

Positive definite solution of the matrix equation X=Q+A^H(I⊗X-C)^(-δ)A