Runge's phenomenon is a mathematical phenomenon discovered by Carle David Tolmé Runge when exploring the error of polynomial interpolation.
Consider the function:
The red curve is the Runge function, the blue curve is a 5th order polynomial, while the green curve is a 9th order polynomial. The approximation only gets worse. |
with a polynomial which has a degree , the resulting interpolation would oscillate toward the end of the interval, i.e. close to -1 and 1. It can even be proved that the interpolation error tends toward infinity when the degree of the polynomial increases: