Vector extrapolation methods. Applications and numerical comparison

The present paper is a survey of the most popular vector extrapolation methods such as the reduced rank extrapolation (RRE), the minimal polynomial extrapolation (MPE), the modified minimal polynomial extrapolation (MMPE), the vector ε-algorithm (VEA) and the topological ε-algorithm (TEA). Using projectors, we derive a different interpretation of these methods and give some theoretical results. The second aim of this work is to give a numerical comparison of the vector extrapolation methods above when they are used for practical large problems such as linear and nonlinear systems of equations.