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Manuscript Title: CHPACK: a package for the manipulation of Chebyshev approximations.
Authors: B. D'Aguanno, A. Nobile, E. Roman
Program title: CHPACK
Catalogue identifier: ACER_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 29(1983)361
Programming language: Fortran.
Computer: CDC CYBER 170/720.
Operating system: NOS 2.0.
RAM: 44K words
Word size: 60
Keywords: General purpose, Minimization, Minimax approximation, Approximation, Chebyshev polynomials, Chebyshev series, Linear differential Equations.
Classification: 4.9.

Nature of problem:
In several physical problems a function is required at many points. If its computation is time consuming it can be better to replace it with a suitable approximation.

Solution method:
The present package uses the technique of Chebyshev series development to evaluate an approximation to a function of one variable on an arbitrary interval. It allows evaluation of the coefficients of the series with assigned accuracy, and manipulations of the series (sum and product of two series, integration, derivation). A routine of the package solves a linear differential equation provided that the coefficients of the equation can be expanded in Chebyshev series. An error estimate is provided in all cases.

Restrictions:
The only restriction is the maximum number of coefficients that can be evaluated, which has been fixed at 124 (this number plays a role only in routine CHCOEF, and can be easily changed as it appears only in a PARAMETER statement), and the maximum relative accuracy (1.E-13), which is connected with the word length.

Running time:
The evaluation of 128 coefficients of a cosine took 0.1 s, including the time for 128 cosine calls. The solution of differential equations depends heavily on the order of the equations and the number of coefficients involved (in general between 1 and 6 s, see the test runs). The product of two Chebyshev series of 70 terms took 0.13 s; the remaining routines execute in less than 0.01 s.