A de Montessus Type Convergence Study for a Vector-Valued Rational Interpolation Procedure of Epsilon Class
Provides theoretical convergence guarantees for a specific rational interpolation method, but is an incremental extension of prior work on related methods.
The paper proves de Montessus and König type convergence theorems for the ITEA vector-valued rational interpolation method when applied to meromorphic functions with simple poles, extending previous results for IMPE and IMMPE.
In a series of recent publications of the author, three interpolation procedures, denoted IMPE, IMMPE, and ITEA, were proposed for vector-valued functions $F(z)$, where $F : \C \to\C^N$, and their algebraic properties were studied. The convergence studies of two of the methods, namely, IMPE and IMMPE, were also carried out as these methods are being applied to meromorphic functions with simple poles, and de Montessus and König type theorems for them were proved. In the present work, we concentrate on ITEA. We study its convergence properties as it is applied to meromorphic functions with simple poles, and prove de Montessus and König type theorems analogous to those obtained for IMPE and IMMPE.