A de Montessus type convergence study of a least-squares vector-valued rational interpolation procedure II (Q977096)

This is one of a series of papers by the same author, where the convergence of vector-valued rational interpolation procedures is studied, in particular those known as IMPE in the literature. The main results of the paper include a de Montessus type theorem, concerning the convergence of the sequence of approximating rational functions, and König type theorems, concerning the denominator polynomials of the rational functions and their distribution of zeros near the limit; these results apply to rational functions \(F\), while in the last section of the paper the author studies the extension of these theorems to meromorphic functions \(F\) in some domain of the complex plane.