Localization of singular points of meromorphic functions based on interpolation by rational functions

In this paper we examine two algorithms for localization of singular points of meromorphic functions. Both algorithms apply approximation by interpolation with rational functions. The first one is based on global interpolation and gives the possibility to determine the singular points of the function on a domain that includes a simple closed contour on which the values of the function are known. The second algorithm, based on piecewise interpolation, establishes the poles and the discontinuity points on the contour where the function values are given.