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.
