Matrix methods for Padé approximation: Numerical calculation of poles, zeros and residues

A representation of the Padé approximation of the Z-transform of a signal as a resolvent of a tridiagonal matrix Jn is given. Several formulas for the poles, zeros and residues of the Padé approximation in terms of the matrix Jn are proposed. Their numerical stability is tested and compared. Methods for computing forward and backward errors are presented.