Recursive Algorithms for Vector Extrapolation Methods

In this work we devise three classes of recursion relations that can be used for implementing some extrapolation methods for vector sequences. One class of recursion relations can be used to implement methods like the modified minimai polynomial extrapolation and the topological epsilon algorithm, another allows implementation of methods like minimal polynomial and reduced rank extrapolation, while the remaining class can be employed in the implementation of the vector E-algorithm. Operation counts and storage requirements for these methods are also discussed, and some related techniques for special applications are also presented. Included are methods for the rapid evaluation of the vector E-algorithm.