Programs in Physics & Physical Chemistry
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|Manuscript Title: An expansion of complicated functions using Chebyshev polynomials suitable for fast calculation.|
|Authors: M.O. Caceres, H.S. Wio, R.J.J. Stamm'ler|
|Program title: FUNEXP|
|Catalogue identifier: ACEE_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 29(1983)261|
|Programming language: Fortran.|
|Computer: IBM 360/44.|
|Operating system: IBM 44PS.|
|RAM: 1K words|
|Word size: 32|
|Keywords: General purpose, Fast evaluation, Chebyshev polynomials, Recurrence relations, Function expansion.|
Nature of problem:
When solving physical and mathematical problems on a computer, one or more complicated functions may have to be evaluated a great number of times. For the sake of computational efficiency it is then desirable to have a fast and compact algorithm for the evaluation of such functions.
Low-order power expansions of high accuracy are used. These are obtained via known relations from Fourier-Chebyshev series in a set of ad hoc chosen intervals. The program described in this paper performs the following tasks.
1) It partitions user-specified argument ranges (macro-intervals) in a given number of small subintervals.
2) In these subintervals, it evaluates the coefficients of Chebyshev expansions up to sixth order.
3) It rearranges the Chebyshev expansions into power series expansions, and computes, per subinterval, the average and maximum error in a given number of points.
The only restrictions on the programs are the number of subintervals in each macrointerval (NI). The combination number, given by 2*NI+132, must not exceed the dimension of the working vector. In the present version, the working vector has been dimensioned to 1000. However, this can readily be changed by the user.
The full test run took 34 s on the IBM 360/44.
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