Some properties of the recursive projection and interpolation algorithms

The recursive projection algorithm (rpa), derived from the vectorSylvester identity, has a connection with the recursive interpolationalgorithm (ria). These algorithms have many applications andconnections with some other methods used in various areas ofnumerical analysis. The aim of this paper is to study some propertiesof these algorithms. We use properties of projectors, a matriximplementation and the Schur complement extended to the vectorcase, to give a result about their finite termination.