Technical Report CS0347

Title: An Algorithm for a Generalization of the Richardson Extrapolation Process
Authors: William F. Ford and Avram Sidi
Abstract: In this paper we present a recursive method, designated the W^(m)-algorithm for implementing a generalization of the Richardson exptrapolation process that has been introduced in [8]. Compared to the direct solution of the linear systems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying the d-transformation of [6,13] to power series. In the course of development a new recursive algoritm for implementing a very general extrapolation procedure is introduced, which is similar to that given in [2,4] for solving the same problem. A FORTRAN program for the W^(m)-algorithm is also appenqed.
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