ABSTRACT
Several procedures for fitting approximating polynomials to a set of tabular data are presented in Sections 4.3 to 4.6. Problems can arise when a single high-degree polynomial is fit to a large number of points. High-degree polynomials would obviously pass through all the data points themselves, but they can oscillate wildly between data points due to round-off errors and overshoot. In such cases, lower-degree polynomials can be fit to subsets of the data points. If the lower-degree polynomials are independent of each other, a piecewise approximation is obtained. An alternate approach is to fit a lower-degree polynomial to connect each pair of data points and to require the set of lower-degree polynomials to be consistent with each other in some sense. This type of polynomial is called a spline function, or simply a spline.
