Matrix methods for Pad\'e approximation: numerical calculation of poles, zeros and residues

Luca Perotti; Michal Wojtylak

arxiv: 1712.01155 · v2 · pith:CTQFYE4Lnew · submitted 2017-12-04 · 🧮 math.NA · math.FA

Matrix methods for Pad\'e approximation: numerical calculation of poles, zeros and residues

Luca Perotti , Michal Wojtylak This is my paper

classification 🧮 math.NA math.FA

keywords approximationmatrixmethodsnumericalpolesresidueszerosbackward

0 comments

read the original abstract

A representation of the Pad\'e 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 Pad\'e 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.

This paper has not been read by Pith yet.

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

On the Inverse Problem in Effective Field Theory
hep-th 2026-04 unverdicted novelty 8.0

The tree-level spectrum of heavy particles can be extracted from EFT Wilson coefficients using new nonlinear analytic dispersion relations, exactly for finite resonances and approximately otherwise.