7 Cubic Splines and Least-Squares Approximation

Section 6 showed that a single polynomial through many points can oscillate badly. This section takes two other routes to fitting data. Splines still pass through every point, but use a different low-degree polynomial on each subinterval, joined smoothly. Least squares gives up passing through the points at all, which is the right choice when the data contain errors of measurement: it finds the simple function that comes closest to them on average.

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