# A de Montessus Type Convergence Study for a Vector-Valued Rational Interpolation Procedure of Epsilon Class

## TL;DR

This paper investigates the convergence properties of the ITEA vector-valued rational interpolation method for meromorphic functions with simple poles, establishing de Montessus and König type theorems similar to previous methods.

## Contribution

It extends convergence analysis and proves de Montessus and König type theorems for the ITEA interpolation procedure, complementing prior work on IMPE and IMMPE methods.

## Key findings

- Proves de Montessus type convergence theorem for ITEA.
- Establishes König type convergence results for ITEA.
- Demonstrates convergence properties for meromorphic functions with simple poles.

## Abstract

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 K\"{o}nig 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 K\"{o}nig type theorems analogous to those obtained for IMPE and IMMPE.