Pole recovery from noisy data on imaginary axis

TL;DR

This paper introduces an algorithm that accurately identifies poles and residues of meromorphic functions from noisy imaginary axis data using Möbius transform and Prony's method, with demonstrated numerical effectiveness.

Contribution

It presents a novel algorithm combining Möbius transform and Prony's method for pole identification from noisy data on the imaginary axis.

Findings

Effective pole and residue recovery demonstrated through numerical experiments

Algorithm handles noisy data robustly

Combines Möbius transform with Prony's method for improved accuracy

Abstract

This note proposes an algorithm for identifying the poles and residues of a meromorphic function from its noisy values on the imaginary axis. The algorithm uses M\"{o}bius transform and Prony's method in the frequency domain. Numerical results are provided to demonstrate the performance of the algorithm.