A Review of Two Algorithms for Acceleration of Convergence of a Sequence of Vectors

摘要

The purposes of this article are threefold: (i) to review the role of Wynn's epsilon algorithm as a method for acceleration of convergence of an ordinary (scalar) series (possibly representing the value of a physical quantity), (ii) to review the role of Wynn's vector-epsilon algorithm and another vector Pade-type method in cases where a number of such series should be treated simultaneously, and (iii) to point out that these general methods for the acceleration of convergence of a vector-valued series are readily applied to the solution of linear and nonlinear systems of equations.