An Algorithm for Spline Interpolation

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Abstract
A detailed description is given of a numerically stable algorithm for the interpolation of equally-or unequally-spaced data by a spline of arbitrary degree. The knots of the spline may be specified in arbitrary positions, as long as a condition relating to the existence of a unique solution is satisfied. In particular, it is not necessary for any of the knots to coincide with data points. For reasons of economy and numerical stability in the formation and solution of the linear equations defining the parameters of the spline, the latter is represented as a linear combination of B-splines. It is shown, however, that for purposes of subsequent rapid evaluation, conversion of the representation into piecewise-Chebyshev-series form is both straightforward and desirable. Numerical examples are appended.

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