A de Montessus type convergence study for a vector-valued rational interpolation procedure (Q926422)

The author continues to study one of the three interpolation procedure that he denotes by IMMPE [cf. J. Approximation Theory 130, No. 2, 179--189 (2004; Zbl 1065.41022)]. The author provides a brief description of the interpolants that result from IMMPE and derived a closed form expression for the error when the function \(F(z)\) being interpolated is rational with simple poles. The author also provides convergence theory for vector-valued rational \(F(z)\) with simple poles and convergence theory for meromorphic \(F(z)\) with simple poles.