Geodesic
Positive definite solution of the matrix equation $X=Q+A^{H}(I\otimes X-C)^{-\delta}A$
The electronic journal of linear algebra, Tome 21 (2010), pp. 76-84.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the nonlinear matrix equation X = Q+A $H(I \otimes X - C) - \delta A (0 \delta \leq 1)$, where Q is an n $\times n$ positive definite matrix, C is an mn $\times $mn positive semidefinite matrix, I is the m $\times m$ identity matrix, and A is an arbitrary mn $\times n$ 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 $\otimes $Q > C. Two bounds for the solution of the equation are derived. This equation is related to an interpolation problem when $\delta = 1$. Some known results in interpolation theory are improved and extended.
Classification : 15A24, 65H05
Keywords: nonlinear matrix equation, positive definite solution, interpolation theory 
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     title = {Positive definite solution of the matrix equation $X=Q+A^{H}(I\otimes X-C)^{-\delta}A$},
     journal = {The electronic journal of linear algebra},
     pages = {76--84},
     publisher = {mathdoc},
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Yao, Guozhu; Liao, Anping; Duan, Xuefeng. Positive definite solution of the matrix equation $X=Q+A^{H}(I\otimes X-C)^{-\delta}A$. The electronic journal of linear algebra, Tome 21 (2010), pp. 76-84. http://geodesic.mathdoc.fr/item/ELA_2010__21__a6/