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Manuscript Title: A cubic spline interpolation of unequally spaced data points.
Authors: J. Anderson, R.W.B. Ardill, K.J.M. Moriarty, R.C. Beckwith
Program title: CUSPLN
Catalogue identifier: ACYV_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 16(1979)199
Programming language: Fortran.
Computer: CDC 6600.
Operating system: CDC SCOPE.
RAM: 18K words
Word size: 60
Peripherals: graph plotter.
Keywords: General purpose, Interpolation, Spline, Cubic spline, Natural cubic spline, Curve length, Differentiation.
Classification: 4.10.

Subprograms used:
Cat Id Title Reference
AAUN_v1_0 APLOT CPC 9(1975)85

Nature of problem:
Quite often an experiment results in a series of discrete data points inthe interval (x0,xN). The theorist then wishes to interpolate this data at some point x epsilon(x0,xN) or at a large number of points covering the domain (x0,xN) so that an interpolating curve may be drawn. The theorist may also wish to interpolate the discrete data points in order to i)calculate the length of the curve through the data points ii)calculate the area under the curve through the data points or iii)calculate the derivative of the curve through the data points over the domain (x0,xN). The most efficient method of accomplishing this is with the cubic spline interpolation function.

Solution method:
The cubic spline interpolation function matrix equations are solved to give the second derivatives at the N+1 discrete data points. From these the cubic spline interpolation function equations in each interval x esiplon [xi,xi+1] (i=0,1,...,N-1) are then constructed. The interpolation, or the first derivative of the interpolation, can then easily be carried out at the point x epsilon [xO,xN].