Consider the nonlinear matrix equation X=Q+A(H)((X) over cap - C)-(1)A, where Q is an n x n Hermitian positive definite matrix, C is an mn x mn Hermitian positive semidefinite matrix, A is an mn x n matrix, and (X) over cap is the m x m block diagonal matrix defined by (X) over cap = diag(X, X,..., X), in which X is an n x 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. (C) 2003 Elsevier Inc. All rights reserved.
2003. Vol. 372, 33-51 p.