Spline Interpolation

Spline interpolation constructs a spline that passes through prescribed data points. Given distinct nodes and values , a cubic spline interpolant satisfies , is a cubic polynomial on every interval , and has continuous first and second derivatives.

Two additional endpoint conditions determine a unique cubic spline. A natural cubic spline uses , while a clamped cubic spline specifies the two endpoint slopes. Spline interpolation generally avoids the large oscillations that can occur with a single high-degree interpolating polynomial.