Spline
A piecewise-polynomial interpolant with smoothness conditions at the joints.
Definition
Instead of one high-degree polynomial, a spline uses a low-degree polynomial on each subinterval and enforces continuity of the function and its derivatives at the nodes. The natural cubic spline is and is the practical standard.
How it is used
It is the standard answer to the Runge phenomenon: with many equispaced nodes, interpolate piecewise instead of raising the degree.