On locating the zeros and poles of a meromorphic function

TL;DR

This paper introduces a stable numerical method based on the generalized argument principle for locating zeros and poles of meromorphic functions, with automatic error estimation and applications in plasma physics.

Contribution

A new subdivision-transformation-calculation algorithm for stable zero and pole detection with automatic error estimation is developed.

Findings

Algorithm successfully locates zeros and poles in numerical examples.

Automatic error estimation enhances reliability of the method.

Potential applications demonstrated in plasma physics contexts.

Abstract

On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A novel feature of this algorithm is the ability to estimate the error level automatically. Numerical examples are also presented, with an emphasis on potential applications to plasma physics.