9

SIAM Journal on Numerical Analysis

1987

24

5

1212-1232

convergence acceleration , generalized Richardson extrapolation , recursive algorithms

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In this paper we present a recursive method, designated the W('")-algorithm, for implementing a generalization of the Richardson extrapolation 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 algorithm 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('n)-algorithm is also appended

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