Perturbation analysis of the matrix equation X=Q+AH(X−C)−1A

AbstractConsider the nonlinear matrix equationX=Q+AH(X−C)−1A,where Q is an n×n Hermitian positive definite matrix, C is an mn×mn Hermitian positive semidefinite matrix, A is an mn×n matrix, and X is the m×m block diagonal matrix defined by X=diag(X,X,…,X), in which X is an n×n matrix. This matrix equation is connected with certain interpolation problem. In this paper, perturbation bounds and condition numbers for the maximal solution are presented, and residual bounds for an approximate solution to the maximal solution are obtained. The results are illustrated by numerical examples