Introduction to the New Type of Algorithms for Accelerating Convergence of Sequence

A collection of new algorithms for accelerating the convergence of sequence of functions was described. The definitions and connections of these new algorithms with the improved functional epsilon algorithms are given. The effectiveness of these new algorithms was examined, namely the α-algorithms, the β-algorithms, the γ-algorithms, the δ-algorithms and the improved functional epsilon algorithms, for approximating solutions of a given power series. The estimates derived using the δ-algorithms are found to be substantially more accurate than other similar algorithms.