The maximal solution (unique Hermitian solution) to the nonlinear matrix equation
is discussed. Here in this equation, stands for an Hermitian matrix, , () with being an Hermitian positive (positive semidefinite) matrix, is an Hermitian positive semidefinite matrix and is the block diagonal matrix defined by , where is an matrix. This matrix equation has significance in interpolation theory.
Some perturbation results (perturbation bounds and condition numbers) for the maximal solution to this matrix equation are presented and residual bounds for an approximate solution to the maximal solution are given. Two numerical examples with , are given as well-conditioned and moderately ill-conditioned numerical cases to support the main presented results.