Matrix methods for Padé approximation: numerical calculation of poles, zeros and residues
Provides a new numerical framework for Padé approximation, relevant to signal processing and systems theory, but the improvements over existing methods are not quantified.
The paper introduces a matrix-based representation of Padé approximations for the Z-transform, enabling numerical calculation of poles, zeros, and residues via a tridiagonal matrix. It proposes and compares several formulas, testing numerical stability and error computation.
A representation of the Padé approximation of the $Z$-transform of a signal as a resolvent of a tridiagonal matrix $J$ is given. Several formulas for the poles, zeros and residues of the Padé approximation in terms of the matrix $J$ are proposed. Their numerical stability is tested and compared. Methods for computing forward and backward errors are presented.