Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours

In the present paper the Padé approximation with Laurent polynomials is examined for a meromorphic function on a finite domain of the complex plane. Values of the function are given at the points of a simple closed contour from this domain. Based on this approximation, an efficient numerical algorithm for locating singular points of the function is proposed.