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GNU Scientific Library Reference Manual - Third Edition (v1.12)
by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi
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ISBN 0954612078
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26.3 Interpolation Types

The interpolation library provides five interpolation types:

Interpolation Type: gsl_interp_linear
Linear interpolation. This interpolation method does not require any additional memory.
Interpolation Type: gsl_interp_polynomial
Polynomial interpolation. This method should only be used for interpolating small numbers of points because polynomial interpolation introduces large oscillations, even for well-behaved datasets. The number of terms in the interpolating polynomial is equal to the number of points.
Interpolation Type: gsl_interp_cspline
Cubic spline with natural boundary conditions. The resulting curve is piecewise cubic on each interval, with matching first and second derivatives at the supplied data-points. The second derivative is chosen to be zero at the first point and last point.
Interpolation Type: gsl_interp_cspline_periodic
Cubic spline with periodic boundary conditions. The resulting curve is piecewise cubic on each interval, with matching first and second derivatives at the supplied data-points. The derivatives at the first and last points are also matched. Note that the last point in the data must have the same y-value as the first point, otherwise the resulting periodic interpolation will have a discontinuity at the boundary.
Interpolation Type: gsl_interp_akima
Non-rounded Akima spline with natural boundary conditions. This method uses the non-rounded corner algorithm of Wodicka.
Interpolation Type: gsl_interp_akima_periodic
Non-rounded Akima spline with periodic boundary conditions. This method uses the non-rounded corner algorithm of Wodicka.

The following related functions are available:

Function: const char * gsl_interp_name (const gsl_interp * interp)
This function returns the name of the interpolation type used by interp. For example,
printf ("interp uses '%s' interpolation.\n", 
        gsl_interp_name (interp));

would print something like,

interp uses 'cspline' interpolation.
Function: unsigned int gsl_interp_min_size (const gsl_interp * interp)
This function returns the minimum number of points required by the interpolation type of interp. For example, Akima spline interpolation requires a minimum of 5 points.
ISBN 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition