A method is described for fitting a piecewise cubic polynomial to a sequence of data by a onepass method. The polynomial pieces are calculated as the data is scanned only once from left to right. The algorithm is shown to be stable when a piecewise cubic polynomial is used which is continuous with its first derivative, while it becomes unstable if the polynomial is made continuous up to the second derivative. The knots of the approximating function are determined successively using a criterion by Powell.
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Ichida et al. (1977) studied this question.