![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Runge_phenomenon.svg/640px-Runge_phenomenon.svg.png&w=640&q=50)
Runge's phenomenon
Failure of convergence in interpolation / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Runge's phenomenon?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In the mathematical field of numerical analysis, Runge's phenomenon (German: [ˈʁʊŋə]) is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901) when exploring the behavior of errors when using polynomial interpolation to approximate certain functions.[1] The discovery shows that going to higher degrees does not always improve accuracy. The phenomenon is similar to the Gibbs phenomenon in Fourier series approximations.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Runge_phenomenon.svg/640px-Runge_phenomenon.svg.png)
The function
A fifth order polynomial interpolation (exact replication of the red curve at 6 points)
A ninth order polynomial interpolation (exact replication of the red curve at 10 points)