An expansion of complicated functions using Chebyshev polynomials suitable for fast calculation
✍ Scribed by Manuel O. Cáceres; Horacio S. Wio; R.J.J. Stamm'ler
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 435 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0010-4655
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✦ Synopsis
Nature of the physical problem
When solving physical and mathematical problems on a corn-Catalogue number: ACEE puter, one or more complicated functions many have to be evaluated a great number of times. For the sake of computa-Program obtainable from: CPC Program Library, Queen's Uni-tional efficiency it is then desirable to have a fast and compact versity of Belfast, N. Ireland (see application form in this issue) algorithm for the evaluation of such functions.
Computer: IBM 360/44; Installation: Centro Atómico Ban-
Method of solution loche Computer Center
Low-order power expansions of high accuracy are used. These are obtained via known relations from Fourier-Chebyshev Operating system: IBM 44PS series in a set of ad hoc chosen intervals. The program described in this paper performs the following tasks. Programming language: FORTRAN IV 1) It partitions user-specified argument ranges (macro-inter-High speed storage required: I Kwords vals) in a given number of small subintervals. 2) In these subintervals, it evaluates the coefficients of No. of bits in a word: 32 Chebyshev expansions up to sixth order. 3) It rearranges the Chebyshev expansions into power series No. of cards in combined program and test deck: 692 expansions, and computes, per subinterval, the average and maximum error in a given number of points.