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Manuscript Title: Fourier analysis with splines. A Fortran program.
Authors: C. Pomponiu, M. Sararu
Program title: TRIINT
Catalogue identifier: AAUX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 16(1978)93
Programming language: Fortran.
Computer: IBM 370/135.
Operating system: DOS.
RAM: 104K words
Word size: 8
Keywords: General purpose, Spline functions, Fourier analysis, Fourier coefficients, Complex functions, Approximation.
Classification: 4.6.

Nature of problem:
There often arises the need for a good trigonometric representation of periodic continuous functions in various areas of physics and engineering. These functions can be given either by a formula or by their values at specified points. The subroutine package TRIINT provides a procedure for fast and accurate Fourier representation for functions of the former class because the discrete case can be treated in a similar way, once a suitable data-interpolation formula is found.

Solution method:
The analysed function is approximated first by a cubic spline interpolant, then the Fourier coefficients of the latter are constructed. Showing a rate of (asymptotic) decrease of 1/n**3 these coefficients provide a good trigonometric approximation of the spline interpolant and of the analysed function itself in so far as the latter is well approximated by the spline interpolant.

The main restrictions concern the dimensions of the arrays used in constructing the spline interpolant and in storing the computed coefficients for testing purposes. For more than 1800 knots the dimensions of ALFA (1800) in subroutine SPLINE and of all arrays in block /SPLTHT/ should be increased accordingly. The same holds true for the arrays in blocks /COEFF/ and /SERVICE/, if more than 501 Fourier coefficients are needed. To save high-speed storage, execution can be forced in single precision by punching C in the first column of all IMPLICIT REAL*8 (A-H,O-Z) and FORTRAN-function defining cards.

Unusual features:
The program was designed to work in stages in order that the user might control the accuracy of the computations as the program goes along, and pass to the next stage when the attained error level proves satisfactory.

Running time:
The Central processor Unit running time for computing 101 coefficients using a 127-knot spline interpolant was about 5 s.