Before revision:  In the second part, we extend the proposed framework to locate the eigenvalues of a general square large-scale nonlinear meromorphic matrix-valued function T(\cdot), where we exploit a representation \mathcal R (s) = C(s) A(s)^{-1} B(s) - D(s) defined in terms of the block components of T(\cdot).
After revision:  In the second part, we extend the proposed framework to locate the eigenvalues of a general square large-scale nonlinear meromorphic matrix-valued function T(\cdot), where we exploit a representation \mathcal{R (s) = C(s) A(s)^{-1} B(s) - D(s) defined in terms of the block components of T(\cdot).