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Manuscript Title: Approximating functions by means of symbolic computation and a general extrapolation method.
Authors: J. Grotendorst
Program title: BH
Catalogue identifier: ABRN_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 59(1990)289
Programming language: Maple.
Computer: IBM 3090-200E.
Operating system: VM/XA SP REL.2.
RAM: 9999K words
Word size: 32
Keywords: Computer algebra, General purpose, Utility, Brezinski-havie protocol, E algorithm, Polynomial and rational Extrapolation Of functions, Series (sequence) Transformations, Symbolic computation, Generation of Fortran functions.
Classification: 4.14, 5.

Nature of problem:
Approximating functions by means of formal series expansions is a technique which is applied quite frequently in the mathematical treatment of physical problems. To improve the quality of the approximation by appropriate extrapolation methods is highly desired.

Solution method:
MAPLE proceduers are presented for transforming the Taylor or asymptotic expansion of a given function into an approximating function using a suitable series transformation. A general extrapolation algorithm due to Brezinski and Havie is used to perform the Richardson extrapolation process, the p transformation of Wynn and the transformations of Shanks, Levin and Germain-Bonne. For numerical purposes the approximating functions can be translated into optimized FORTRAN function programs.

Restrictions:
The available computer storage is the severest restriction.