Runge phenomenon

Growing oscillations near the endpoints when interpolating with high degree at equispaced nodes.

Definition

As the interpolant's degree grows over equispaced nodes, the error can grow without bound near the ends of the interval, as the classic example f(x)=1/(1+25x2)f(x)=1/(1+25x^2) on [1,1][-1,1] shows. More nodes does not mean a better approximation.

How it is used

It is the warning that high degree on equispaced nodes is dangerous: use splines or Chebyshev nodes, which cluster points near the endpoints.