Locating Poles of Rational Functions in the Half Plane by Using the Backward Shift Operator

ABSTRACT In this study, we propose a method for locating poles of rational functions within the half‐plane. This work extends the previous research on the backward shift algorithm developed for Hardy spaces in the unit disc. For rational functions, repeated application of the backward shift operator eventually yields an algebraic equation. The solutions of this equation precisely correspond to the poles of the original function, capturing both their locations and multiplicities. Based on this observation, we introduce an approach to determine these poles using discrete boundary data from the half‐plane. We analyze the approximation error and prove the convergence of the proposed method.