Determination of poles of sectionally meromorphic functions (Q1820552)

The author proposes a method for locating the poles (and, in a special case, the zeros) inside a closed smooth curve C of a function F meromorphic except for discontinuities along some other smooth closed curves (which may intersect C), where F is assumed to satisfy a Riemann- Hilbert problem with known Hölder-continuous coefficients. First, the values on C of another function R with the same poles as F but no other discontinuities are constructed, and then a method of \textit{L. Abd-Elall}, \textit{L. Delves} and \textit{J. Reid} [Numerical methods for nonlinear algebraic equations, Conf. Univ. Essex 1969, 47-59 (1970; Zbl 0245.65019)] is applied to R. Two simple applications illustrate the method.