Algorithm 472 Procedures for Natural Spline Interpolation [El].

The article presents a computer algorithm related to procedures for natural spline interpolation. The purpose of the procedures that have been presented is to determine the interpolating natural spline function for a set of data points. The interpolating natural spline functions are polynomials and their derivatives are continuous functions. The algorithm computes the coefficients of the natural spline for several cases. The algorithm treats the case of equidistant knots. If the knots are known to be equidistant, the use of this procedure results in considerable economy of computational effort. Since the case of a cubic natural spline is of frequent occurrence, a procedure has been given that computes the coefficients in this special case. This procedure is very much faster than either of the other procedures. The calculation of the coefficients is carried out in a numerically stable manner. For convenience of calculations, a normalizing factor has been used. The parameters that have been used in the algorithm have been described.