For a given finite set of points
$$(z_j)_{j=1}^N$$
in the complex plane and their corresponding values
$$(f_j)_{j=1}^N$$
there are many methods to construct a meromorphic function $f$ such that
$$f(z_j) = f_j, ~j=1,..,N$$
One such method is called Nevanlinna interpolation (see the attachedlinks for details). My question is: Does there exist a systematic method to determine the poles of the function obtained via Nevanlinna interpolation?
https://huangli712.github.io/projects/acflow/theory/nac.html#nac
https://en.wikipedia.org/wiki/Nevanlinna%E2%80%93Pick_interpolation
For a given finite set of points
in the complex plane and their corresponding values
there are many methods to construct a meromorphic function$f$ such that
One such method is called Nevanlinna interpolation (see the attachedlinks for details). My question is: Does there exist a systematic method to determine the poles of the function obtained via Nevanlinna interpolation?
https://huangli712.github.io/projects/acflow/theory/nac.html#nac
https://en.wikipedia.org/wiki/Nevanlinna%E2%80%93Pick_interpolation