Convergence and Stability Properties of Minimal Polynomial and Reduced Rank Extrapolation Algorithms

The minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods far sequences of vectors. In a recent survey these methods were tested and compared with the scalar, vector, and topological epsilon algorithms, and were observed to be more efficient than the latter. It was also observed that the two methods have similar convergence properties. The purpose of the present work is to analyze the convergence and stability properties of these methods, and to show that they are bona fide acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods.