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LOCALIZATION OF SINGULAR POINTS OF MEROMORPHIC FUNCTIONS BASED ON INTERPOLATION BY RATIONAL FUNCTIONS
(2021) Capcelea, Maria; Capcelea, Titu
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.
LAURENT-PAD ́E APPROXIMATION FOR LOCATING SINGULARITIES OF MEROMORPHIC FUNCTIONS WITH VALUES GIVEN ON SIMPLE CLOSED CONTOURS
(Institutul de Matematică şi Informatică al AŞM, 2020) Capcelea, Maria; Capcelea, Titu
In the present paper the Pad ́e approximation with Laurent polynomials is examined for a meromorphic function on a finite domain of the c omplex plane. Values of the function are given at the points of a simple closed cont our from this domain. Based on this approximation, an efficient numerical algorith m for locating singular points of the function is proposed.